the spectrum of mechanics

The general study of the relationships between motion, forces, and energy is called mechanics . It is a large field and its study is essential to the understanding of physics, which is why these chapters appear first. Mechanics can be divided into sub-disciplines by combining and recombining its different aspects. Some of these are given special names.

Motion is the action of changing location or position. The study of motion without regard to the forces or energies that may be involved is called kinematics . It is the simplest branch of mechanics. The branch of mechanics that deals with both motion and forces together is called dynamics and the study of forces in the absence of changes in motion or energy is called statics .

The term energy refers an abstract physical quantity that is not easily perceived by humans. It can exist in many forms simultaneously and only acquires meaning through calculation. Informally, a system possesses energy if it has the ability to do work. The energy of motion is called kinetic energy .

Whenever a system is affected by an outside agent, its total energy changes. In general, a force is anything that causes a change (like a change in energy or motion or shape). When a force causes a change in the energy of a system, physicists say that work has been done. The mathematical statement that relates forces to changes in energy is called the work-energy theorem .

When the total of all the different forms of energy is determined, we find that it remains constant in systems that are isolated from their surroundings. This statement is known as the law of conservation of energy and is one of the really big concepts in all of physics, not just mechanics. The study of how energy changes forms and location during physical processes is called energetics , but the word is used more by scientists in fields outside of physics than inside.

The first few chapters of this book are basically about these topics in this order…

  • motion (kinematics)
  • forces (dynamics and statics)

types of motion

Motion may be divided into three basic types — translational, rotational, and oscillatory. The sections on mechanics in this book are basically arranged in that order. The fourth type of motion — random — is dealt with in another book I wrote.

the physics

Moving words, mechanics, dynamics, statics, kinematics.

The words mechanics, dynamics, statics, and kinematics are used throughout this book and heavily in the first third. Each refers to a discipline or branch of physics, thus the common suffix -ics. Each word can also be changed from a noun to an adjective. This gives us words like dynamic, static, kinematic, mechanical, dynamical, and physical. We can also make adverbs like dynamically and physically. Here are the relevant nouns, each followed by brief definition and a semi-long-winded story about its origin. For many readers, the brief definitions will be good enough.

This organizational scheme is incomplete as far as I'm concerned. It's missing one key concept, possibly the most important concept in all of mechanics, possibly in all of physics, possibly in all of science — energy. Because energy arose as a concept after this scheme was created, a name was never assigned to the branch of mechanics dealing with energy. There is a word energetics, but it doesn't seem to be popular in general physics textbooks. The equivalent concept in general physics is called thermodynamics, which started out as the study of work done by thermal processes but expanded into the more general law of conservation of energy.

Here's an oddball word that I don't know how to handle.

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types of motion essay

by Chris Woodford . Last updated: October 22, 2022.

Photo: A space rocket is an impressive demonstration of Newton's laws of motion. The force of the hot exhaust gas shooting backward propels the rocket forward. The rocket isn't moving by pushing against the ground; it can move forward like this even in "empty space," confirming the essential truth of Newton's laws. Photo, of a proton booster rocket blasting off with a component of the International Space Station, courtesy of NASA on the Commons .

Photo: Forces are the power behind our world. Thump an object with a big enough force and it will accelerate to a very high speed. That's the basic idea behind bullets and missiles like the one blasting from this replica of an 1855 cannon. Photo by Mollie Miller published under a Creative Commons Licence courtesy of US Army/Flickr .

A force is a pushing or pulling action that can make things move, change direction, or change shape .

Photo: In soccer, several different forces power the ball from your foot to the goal. Photo by Justin M. Boling courtesy of US Marine Corps .

Artwork: Bridges are giant static structures, but that doesn't mean they're force free. Bridges carry loads by balancing them with stretching forces (tension, shown in blue), squashing forces (compression, shown in red), or both. Different types of bridges do this in different ways. In a suspension bridge, the towers are in compression (squashed down) while the huge cables that support them are in tension (pulling tight).

Photo: Resultant force: In this tug-of-war, if the red team pulls left with a strong force and the orange team pulls right with a weaker force, there is an overall force to the left (white). This is called the resultant force and it's equal to the red force minus the orange force. Photo by Grace Riegel courtesy of DVIDS .

Photo: Hurricanes are powered by force. The air pressure is higher at the edge than in the middle, creating a force toward the center—centripetal force—that makes the air rotate at high speed. This photo shows Hurricane Fran heading for North Carolina and Virginia in August 1989; it went on to cause about $5 billion worth of damage. Photo courtesy of NASA on the Commons .

Artwork: Spin-drying laundry uses the power of centripetal force. 1) A clothes washing machine has a rotating drum (white) with holes in it mounted inside a static drum (red) that's completely sealed. 2) As the inner drum spins, it pushes your clothes round in a circle, supplying the centripetal force that makes them turn. 3) The water inside the clothes can move freely and there's no centripetal force to make it move in a circle, so it flies off in straight lines through holes in the drum. 4) The water collects in the outer drum. 5) At the end of the spin cycle, the water pumps out through a drain pipe.

Photo: The soles of your shoes are designed to maximize friction—or you'd fall over every time you took a step forward.

Changing materials

Photo: A digger like this magnifies forces using hydraulics: it squirts a liquid through hydraulic cables and pipes (blue) to operate the hydraulic rams (red) that push and pull the arm and bucket.

Newton's three laws of motion

Photo: Isaac Newton—the man who put science in motion. Picture from an 18th-century engraving by William Thomas Fry courtesy of US Library of Congress .

Newton's laws in practice

Photo: Another example of Newton's laws: 1) The tractor stays still unless a force acts on it. 2) When this boy (and his friends, who are out of shot to the left) supply a force by pulling on the rope, the tractor accelerates toward them. 3) When the boys pull on the rope, the tractor pulls back: that's what keeps the rope taut. Does that seem confusing? Think of it this way. Before the boy's friends arrive, he pulls by himself on the rope and can't move the tractor. The boy pulls the rope to the left, the tractor pulls it to the right, the two forces balance, and the tractor goes nowhere.

Only motion

Measuring motion, acceleration, kinetic energy, what is an impulse, the sporting impulse.

Photo: Think sport? Think impulse! If you want to hit a ball as far as possible, you need to apply a force with your muscles for as long as possible: you can't change the mass (m) of the ball, but you can maximize the time (t) during which the bat touches the ball as well as the force (F) to give the ball as big a velocity (v = F t / m) as possible. Photo by Shannon McMillan courtesy of US Marine Corps .

If you liked this article...

Don't want to read our articles try listening instead, find out more, on this website.

  • Brakes : How do you get rid of motion when you don't want it?
  • Bullets : How can we use the laws of motion to understand how bullets fly?
  • The law of conservation of energy : Why can we create or destroy energy?
  • Energy : What is energy anyway?
  • Gears : Why can you make a machine go faster or increase the force it produces, but not both at the same time?
  • Science of sport : How the laws of motion can help us understand sports like tennis, baseball, running, and swimming.

For younger readers

  • A Crash Course in Forces and Motion by Emily Sohn. Capstone, 2019. The graphic-novel style of this 32-page introduction should appeal to reluctant readers and children who prefer comics to books. Described as suitable for ages 8–14.
  • Can you Feel the Force? by Richard Hammond. New York/London: Dorling Kindersley, 2007/2015. A good, slightly irreverent introduction to basic physics, including Newton's laws. Ages 8–10.
  • Thud! Wile E. Coyote Experiments with Forces and Motion by Mark Weakland. Capstone, 2014. Another simplified, visual introduction that will appeal to young, reluctant readers; 32 pages for ages 8–14.
  • Forces and Motion: Investigating a Car Crash by Ian Graham. Raintree, 2014. A great example of how Newton's laws are used in the real world. With an engaging graphic novel format, this is another good choice for reluctant readers and children who struggle to find science relevant.
  • Fatal Forces by Nick Arnold. Scholastic, 2014. A funny, cheeky guide to forces from the popular Horrible Science series. For ages 10–12, 128 pages.
  • Science Investigations: Forces and Motion by Chris Oxlade. Wayland/Rosen, 2008. An alternative look at basic mechanics. Ages 8–10.

For older readers

  • Newtonian Mechanics by A.P. French. W. W. Norton, 1971. Excellent, classic introduction for undergraduates, but not overly difficult for high-school readers. Don't worry that it's an old book; it's still in print and easy to obtain—and Newton's laws haven't dated in 300 years! This is the book I learned from as a physics student.
  • Physics: Algebra/Trig by Eugene Hecht. Thomson-Brooks/Cole, 2003. I came across the first edition of this book by accident when I was writing some physics articles in the 1990s and really admired the clarity of the text and illustrations and the comprehensive coverage (you'll find virtually every aspect of physics in here somewhere). Eugene Hecht does a very good job of conveying concepts clearly and briefly, with easy-to-understand math, and plenty of real-world examples. Ideally suited to high-school students (ages 16–18), though also good for older readers and brighter youngsters. It's relatively easy to find cheap secondhand early editions of this book if you can't afford the latest version.

On other sites

  • Laboratory Notebook by Isaac Newton : Read Newton's handwritten lab notes in this digital facsimile at the Cambridge University Digital Library.

Text copyright © Chris Woodford 2009, 2022. All rights reserved. Full copyright notice and terms of use .

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Types of Motion

What is motion.

A motion is defined by the change in an object’s position with time. Anything that moves is considered motion. Everything we see in front of us involves motion of some sort. A book falling off a table, the Moon revolving around the Earth, and a racing car on its track all describe motion. The physical quantities that define motion include distance, displacement , speed, and time.

What are the Types of Motion

types of motion essay

1. Translational Motion

In a translational motion , all points of a rigid body move in tandem. In other words, all points move with the same velocity . If the velocity changes or if the object accelerates, all points accelerate at the same time.

Translational motion can be rectilinear and curvilinear .

In a rectilinear motion, all points move in a straight line. For example, a train moving on its track or a bowling ball rolling down an alley.

In a curvilinear motion, all points move in a curved path, For example, a racing car near a turn or a merry-go-round.

2. Rotational Motion

In a rotational motion , all points of an object move in a circle. The rotation occurs about an axis; all points move with a common angular velocity . The axis remains fixed in space. For example, a spinning top or Earth rotating about its axis.

3. Oscillatory Motion

In an oscillatory motion , the object moves back and forth about an equilibrium position. Such motion is possible only when a restoring force or torque acts on the object to bring it back to equilibrium. For example, water sprinklers or the vibrations of guitar strings.

4. Periodic Motion

In a periodic motion, the object’s motion is repeated over periodic time intervals. The time interval over which the motion recurs is called the time period. For example, a tuning fork or a simple pendulum .

Other types of motion include:

Uniform motion – When an object covers equal distances in equal intervals of time. For example, a car moves at a constant speed on the highway.

Non-uniform motion – When an object does not cover equal distances in equal time intervals. For example, a ball falls freely from the sky.

  • Motion – Physics.info
  • Types of Motion – Explaining the Basics – Progressiveautomations.com
  • Rotational Motion (Physics): What is it & Why it Matters – Sciencing.com
  • Oscillatory Motion – Phys.libretexts.org

Article was last reviewed on Tuesday, November 21, 2023

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Different Types of motion in Physics with Examples

Types of motion

Basically, there are three types of Motion, Translatory motion, Rotatory motion, and Vibratory motion. Some Other Examples of Motion are Linear motion, Random motion, Circular motion, Uniform, and Non-Uniform Motion . This post also includes lots of:

  • Motion definition
  • Real-life motion examples

So if you want to learn Motion and Type of Motion , You’ll love this post. Let’s dive right in.

What is motion in Physics?

Surroundings are the places in their neighborhood where various objects are present. The state of rest or motion of a body is relative. For example, a passenger sitting on a moving bus is at rest because he is not changing his position with respect to other passengers or objects on the bus. But to an observer outside the bus, the passengers and the objects inside the bus are in motion. Therefore we can define rest as “A body is said to be at rest if it does not change its position with respect to its surroundings. We live in a universe of continual motion. In every piece of matter, the atoms are in a state of never-ending motion. We move around the Earth’s surface, while the earth moves in its orbit around the sun. The sun and the stars, too, are in motion. Everything in the vastness of space is in a state of perpetual motion. Every physical process involves the movement of some sort. Because of its importance in the physical world around us. It is logical that we should give due attention to the study of motion. Motion is commonly described in terms of:

  • Displacement

See also: Difference between distance and displacement

How many types of motion in physics?

Examples of motion

If we observe carefully, we will find that everything in the universe is in motion . However, different objects move differently. Some objects move along a straight line, some move in a curved path, and some move in some other way. According to this, we can say that there are three types of motion. Which are given as:

  • Translatory motion
  • Rotatory motion
  • Vibratory motion

What is Translatory motion?

“In translational motion , a body moves along a line without any rotation. The line may be straight or curved.”Watch how various objects are moving. Do they move along a straight line? Do they move along a circle? A car moving in a straight line has transnational motion. Similarly, an airplane moving straight is in translational motion. Translatory motion is further divided into linear motion, circular motion, and random motion.

Tranaslatory motion Examples

  • Motion of train
  • motion of earth
  • motion of birds
  • motion of insects
  • motion of airplane
  • the motion of gas molecules

Learn more about: Difference between uniform and non-uniform motion

What is Linear motion?

“Straight-line motion of a body is known as its linear motion.”

linear motion

We come across many objects which are moving in a straight line. The motion of objects such as cars moving on a straight and level road is linear motion. Airplanes flying straight in the air and objects falling vertically down are also examples of linear motion. In the above diagram, a boy is sliding in a straight line which is an example of linear motion.

Linear motion examples in daily life

  • The motion of the car on the road
  • Motion of football
  • Sliding a boy in a straight line is an example of linear motion

Read Also: Laws of motion

Circular motion

circular motion

Examples of circular motion in daily life

  • The motion of the electron around the nucleus
  • The motion of the toy car on the circular track
  • The motion of planets around the sun

Random motion

“The disordered or irregular motion of a body is called random motion.”Have you noticed the type of motion of insects and birds? Their movements are irregular and disorderly. The motion of insects and birds is a random motion example. The motion of dust or smoke particles in the air is also a random motion. The Brownian motion of a gas or liquid molecules along a zig-zag is also an example of random motion.”The random motion of gas molecules is called Brownian motion.” This may help you: Equations of motion

What is Rotatory motion?

rotational motion

Rotatory motion examples

  • The motion of the earth about its geographic axis that causes day and night is rotatory motion.
  • The motion of the wheel about its axis and that of the steering wheel are examples of rotatory motion.

What is Vibratory motion?

vibratory motion

  • Difference between spe ed and velocity
  • Difference between positive and negative Acceleration
  • Newton’s three laws of motion
  • Newton’s second law of motion examples and equation
  • Newton’s third law of motion examples 
  • Simple harmonic motion (SHM) examples and formulas
  • Projectile motion equations
  • Difference between distance and displacement

Physics Related Links:

  • The first law of thermodynamics
  • Diffraction of light
  • Difference between convex and concave lens
  • Applications of transistor
  • Coulomb’s law
  • Maxwell’s equations

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Second equation of motion, list of famous physics scientists, kinematic equations in physics list, what is the international system of units, 14 comments.

  • Pingback: Conservative and non conservative forces – Physics Theories Laws Basic Concepts & Resources with major branches
  • Pingback: Mechanics and its branches

Some of this is confusing and some is wrong. Why are insects said to be random and linear? Why is Earth said to be translatory and why is that spelled wrong?

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Newton’s first law: the law of inertia

  • Newton’s second law: F = ma
  • Newton’s third law: the law of action and reaction
  • Influence of Newton’s laws

Isaac Newton: three laws of motion

What are Newton’s laws of motion?

  • What is Isaac Newton most famous for?
  • How was Isaac Newton educated?
  • What was Isaac Newton’s childhood like?

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Newton’s laws of motion

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  • Table Of Contents

Isaac Newton: three laws of motion

Newton’s laws of motion relate an object’s motion to the forces acting on it. In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

Why are Newton’s laws of motion important?

Newton’s laws of motion are important because they are the foundation of classical mechanics, one of the main branches of physics . Mechanics is the study of how objects move or do not move when forces act upon them.

Newton’s laws of motion , three statements describing the relations between the forces acting on a body and the motion of the body, first formulated by English physicist and mathematician Isaac Newton , which are the foundation of classical mechanics .

types of motion essay

Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force . In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle and the other moving at constant velocity with respect to the particle. This postulate is known as the law of inertia .

The law of inertia was first formulated by Galileo Galilei for horizontal motion on Earth and was later generalized by René Descartes . Although the principle of inertia is the starting point and the fundamental assumption of classical mechanics, it is less than intuitively obvious to the untrained eye. In Aristotelian mechanics and in ordinary experience, objects that are not being pushed tend to come to rest. The law of inertia was deduced by Galileo from his experiments with balls rolling down inclined planes.

For Galileo, the principle of inertia was fundamental to his central scientific task: he had to explain how is it possible that if Earth is really spinning on its axis and orbiting the Sun, we do not sense that motion. The principle of inertia helps to provide the answer: since we are in motion together with Earth and our natural tendency is to retain that motion, Earth appears to us to be at rest. Thus, the principle of inertia, far from being a statement of the obvious, was once a central issue of scientific contention . By the time Newton had sorted out all the details, it was possible to accurately account for the small deviations from this picture caused by the fact that the motion of Earth’s surface is not uniform motion in a straight line (the effects of rotational motion are discussed below). In the Newtonian formulation, the common observation that bodies that are not pushed tend to come to rest is attributed to the fact that they have unbalanced forces acting on them, such as friction and air resistance.

types of motion essay

motion: Types of Motion

  • Types of Motion

Uniform motion is motion at a constant speed in a straight line. Uniform motion can be described by a few simple equations. The distance s covered by a body moving with velocity v during a time t is given by s = vt. If the velocity is changing, either in direction or magnitude, it is called accelerated motion (see acceleration ). Uniformly accelerated motion is motion during which the acceleration remains constant. The average velocity during this time is one half the sum of the initial and final velocities. If a is the acceleration, v o the original velocity, and v f the final velocity, then the final velocity is given by v f = v o + at. The distance covered during this time is s = v o t + 1⁄2 at 2 . In the simplest circular motion the speed is constant but the direction of motion is changing continuously. The acceleration causing this change, known as centripetal acceleration because it is always directed toward the center of the circular path, is given by a = v 2 / r, where v is the speed and r is the radius of the circle.

Sections in this article:

  • Introduction
  • The Laws of Motion and Relativity
  • Bibliography

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2024, Columbia University Press. All rights reserved.

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Types of Motion: Definition & Examples

types of motion essay

  • Updated on  
  • Jan 18, 2024

Types of Motion

Let us consider, that you are sitting on your sofa watching TV, think about whether you are in motion or at rest. You are at rest. But let us re-evaluate a situation where the earth is in motion and we are sitting still. Finding the answer to such perplexing questions can be confusing. Before you gear up to find the answer to such complex questions, you must gather thorough knowledge about various types of motion . Here is a blog that aims to elucidate the same with examples that can help you in various competitive and entrance exams 410 .

This Blog Includes:

What is motion , types of motion, oscillatory motion, rotational motion, translational motion, periodic motion , circular motion , linear motion , uniform motion , non-uniform motion .

The free movement of a body concerning time is known as motion. For example fan, the dust falling from the carpet, the water that flows from the tap, a ball rolling around, a moving car etc. Even the universe is in continual motion. Are all these motions the same? Is the motion of a pendulum the same as that of a moving car or train? Various types of motions are happening around us and they can be distinguished based on:

Also Read: Basic Physics Formulas & Notes for Competitive Exams !

As per physics and mechanics, there are mainly 4 types of motion, i.e.

  • Rotary Motion : A special type of motion in which the object is on rotation around a fixed axis like, a figure skater rotating on an ice rink.
  • Oscillatory Motion : A repeating motion in which an object continuously repeats in the same motion again and again like a swing.
  • Linear Motion : A one-dimensional motion on a straight line, like an athlete running on a straight track.
  • Reciprocating Motions : A repetitive and continuous up and down or back and forth motion like a needle in a sewing machine.

Also Read: Essay on Albert Einstein

There are also different other types of motion as per directions or as per state of motion.

Types of motion as per state

  • Non-Uniform Motion

Types of motion as per direction

  • One Dimensional Motion
  • Two Dimensional Motion
  • Three Dimensional Motion

Other types of motion

Here is a chart on types of motion:

Other Types of Motion

Below we have explained the major 7 types of motion as per Physics:

Oscillatory motion is simply the motion that an object does by repeating the same movement again and again. Oscillatory motion would keep on moving forever when there is an absence of friction but in our real world, the motion eventually stops and comes to an equilibrium. Some of the best examples of Oscillatory Motion are:

  • A swinging swing
  • The motion of a pendulum
  • A boat tossing up and down a river
  • The tuning fork

Rotational motion can be defined as when an object moves along its axis and all the parts of it move for a different distance in a given period. Thus, if an object is under rotational motion all of its parts will move different distances in the same interval of time. As an example, merry-go-round, blades of a fan, blades of a windmill etc. 

Also Read: Physics Project for Class 12

When all the parts of an object move the same distance in a given time is known as transitional motion. For example, a cycle moving on a track, a man walking on the road, birds flying in the sky.

Translational Motion

Mainly, there are two types of translation motion which are explained below: 

When an object moving in translational motion follows a curved path it is known as Curvilinear motion. An object moving in translation motion opts a straight-line path, then it is known as Rectilinear motion.
Example: A stone thrown up in the air  Example: A train moving on a straight track or a car moving on a straight road

Also Read: Experiment With Diverse Career in Physics

Periodic Motion Examples

A motion that repeats itself after equal intervals of time is known as periodic motion. Commonly, the objects under this motion are mostly in the to and fro motion. Here are a few examples of periodic motion.

  • A moving pendulum
  • Hands of a working clock
  • the earth rotating on its axis, etc. 

Periodic Motion

Also Read: List of Competitive Exams after 12th

When an object is constantly moving in circular a path it is called circular motion. It circular motion, the speed of the object should be constant. A few examples of circular motion are:

  • Movement of the earth on its axis
  • a bicycle or a car moving on a circular track of the park
  • the motion of the moon around the earth etc.

Also Read: BSc Physics

Linear motion can be defined as the movement of a body in a straight line without any deviation.  Important examples of linear motion are:

  • An athlete running on a straight track in a park
  • a bullet shot from a pistol

A body is said to be in a state of uniform motion when it covers an equal amount of distance in equal intervals of time. In such cases, if we represent the motion on the graph, it would be a straight line. Examples of uniform motion are:

  • A car moving on a straight road at a steady speed
  • a flying aeroplane at a set height at a constant speed, etc

Uniform Motion

Non-uniform motion can be defined as when a given body is covering unequal distances in a set and given intervals of time. If you represent the path of a body moving in non-uniform motion on a graph, it will be a curved line. Examples of non-uniform motion are:

  • a man walking on the road
  • a freely falling body
  • a train moving at various speed limits, etc.

General motion is the most common type of motion in sport and physical exercise.

All motions are relative to a reference frame. Saying that a body is at rest, or that it is not in motion, simply means that it is being described a frame of reference that is moving along with it.

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12 comments

It very very good

I love this, thanks

Yea i understand a bit,little.im from Zimbabwe and currently doing physics.indeed this is helpful.

Thanks for reading. Also, check: Motion in a Plane Laws of Motion Class 11

Thanks for learning about motion.

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types of motion essay

Motion in physics refers to the change in position of an object over time relative to a reference point. It involves the concepts of displacement, velocity, acceleration, and time , and can be described in terms of linear, rotational, or oscillatory movements. Understanding motion is fundamental to physics, as it helps explain how and why objects move, interact, and respond to forces, providing a basis for studying various physical phenomena and principles. This includes the application of Newton’s Laws of Motion , particularly Newton’s Second Law of Motion which relates force, mass, and acceleration, and Newton’s Third Law of Motion which states that for every action, there is an equal and opposite reaction.

What Is Motion?

Motion is the change in an object’s position over time relative to a reference point. It involves displacement, velocity, and acceleration, and is influenced by various forces. Motion is a fundamental concept in physics, describing everything from simple movements to complex orbits.

Motion Formulas

Motion in physics can be described using several key formulas that relate displacement, velocity, acceleration, and time. Here are the essential formulas:

Distance (s):

where s  is distance, v  is velocity, and t  is time.

Velocity (v):

where v  is velocity, Δx  is displacement, and Δt  is time interval.

Acceleration (a):

where aa a is acceleration, Δv  is change in velocity, and Δt  is time interval

Equation of Motion (with initial velocity uu u ):

where s  is displacement, u  is initial velocity, a  is acceleration, and t  is time.

Final Velocity (v):

where v  is final velocity, u  is initial velocity, a  is acceleration, and t  is time.

Examples of Motion

  • Car Driving on a Highway: A car moving in a straight line on a highway represents linear motion.
  • Falling Object: An apple falling from a tree exhibits linear motion due to gravity.
  • Spinning Top: A top rotating around its axis displays rotational motion.
  • Earth’s Rotation: The Earth rotating on its axis, causing day and night, is an example of rotational motion.
  • Pendulum: A pendulum swinging back and forth in a clock exhibits oscillatory motion.
  • Vibrating Guitar String: A plucked guitar string vibrating to produce sound shows oscillatory motion.
  • Thrown Ball: A ball thrown into the air follows a curved path, showing projectile motion.
  • Cannonball: A cannonball fired from a cannon travels in a parabolic trajectory, demonstrating projectile motion.
  • Ferris Wheel: The cabins of a Ferris wheel moving in a circular path demonstrate circular motion.
  • Satellite Orbit: A satellite orbiting around the Earth follows circular motion.
  • Roller Coaster: A roller coaster moving along its track, experiencing various types of motion such as linear and circular motion.
  • Bouncing Ball: A ball bouncing up and down on the ground exhibits oscillatory motion.
  • Swinging Child: A child swinging back and forth on a playground swing demonstrates periodic motion.
  • Helicopter Blades: The blades of a helicopter rotating to generate lift are an example of rotational motion.
  • Running Athlete: An athlete sprinting on a track represents linear motion.
  • Clock Hands: The hands of an analog clock moving in a circular path show circular motion.
  • Diving Dolphin: A dolphin leaping out of the water and diving back in follows projectile motion.
  • Windmill: The blades of a windmill rotating in the wind exhibit rotational motion.
  • Seesaw: A seesaw moving up and down with children on either end shows oscillatory motion.
  • Cycling: A person riding a bicycle involves both linear motion (forward movement) and rotational motion (spinning wheels).
  • Boat on Waves: A boat rocking back and forth on ocean waves exhibits oscillatory motion.
  • Mars Rover: The Mars Rover moving across the surface of Mars demonstrates linear motion.
  • Swinging Lantern: A lantern hanging and swinging in the wind displays periodic motion.
  • Wind Blowing Leaves: Leaves being carried and twirling by the wind show random linear motion and rotational motion.
  • Merry-Go-Round: Horses on a merry-go-round moving in a circular path demonstrate circular motion.

Laws of Motion

1. newton’s first law of motion (law of inertia):.

An object at rest will remain at rest, and an object in motion will continue moving at a constant velocity, unless acted upon by an external force. Example: A book lying on a table will stay at rest until someone applies a force to move it. Similarly, a hockey puck sliding on ice will keep moving in a straight line until friction or another force slows it down.

2. Newton’s Second Law of Motion (Law of Acceleration):

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, F=maF = maF=ma, where FFF is the force, mmm is the mass, and aaa is the acceleration. Example: Pushing a car with more force will cause it to accelerate faster, but the same force applied to a truck will result in less acceleration due to the truck’s greater mass.

3. Newton’s Third Law of Motion (Action and Reaction):

For every action, there is an equal and opposite reaction. This means that forces always occur in pairs. Example: When you jump off a boat, you push the boat backward (action), and the boat pushes you forward with an equal force (reaction). Similarly, when a rocket expels gas downward (action), the rocket is propelled upward (reaction).

Types of Motion

Types of Motion

Motion can be categorized into several types based on the nature of the movement and the forces involved. Here are the main types:

  • Linear Motion : Linear motion occurs when an object moves along a straight path. This can be uniform (constant speed) or non-uniform (changing speed ). Examples include a car driving on a straight road and a ball rolling down a hill.
  • Circular Motion : Circular motion happens when an object moves along a circular path. This includes both uniform circular motion (constant speed around a circle) and non-uniform circular motion (changing speed). Examples include the rotation of a wheel and the orbit of a planet around the sun.
  • Rotational Motion : Rotational motion occurs when an object spins around an internal axis. Examples include a spinning top, the rotation of Earth on its axis, and the turning of a merry-go-round.
  • Oscillatory Motion : Oscillatory motion involves an object moving back and forth around a central point or equilibrium position. Examples include the swinging of a pendulum, the vibration of a guitar string, and the movement of a piston in an engine.
  • Periodic Motion : Periodic motion is a type of oscillatory motion that repeats at regular intervals. Examples include the motion of a clock’s pendulum, the orbits of planets, and the cycles of a sine wave.
  • Random Motion : Random motion is characterized by erratic, unpredictable movement. Examples include the movement of gas molecules in the air and the motion of pollen grains in water (Brownian motion).

Causes of Motion

  • Gravitational Force : The attractive force between two masses (e.g., Earth’s gravity pulling objects downward).
  • Frictional Force : The force that opposes the motion of an object (e.g., a sliding book coming to a stop).
  • Applied Force : A force applied to an object by another object or person (e.g., pushing a cart).
  • Normal Force : The support force exerted upon an object in contact with another stable object (e.g., a book resting on a table).
  • Tension Force : The force transmitted through a string, rope, cable, or wire when it is pulled tight (e.g., a rope in a tug-of-war).
  • Air Resistance Force : A type of frictional force that acts upon objects as they travel through the air (e.g., a parachute slowing down descent).
  • Electromagnetic Forces : Forces associated with electric and magnetic fields (e.g., magnets attracting or repelling each other).
  • First Law (Law of Inertia) : An object at rest stays at rest, and an object in motion stays in motion unless acted upon by an external force.
  • Second Law (Law of Acceleration) : The acceleration of an object depends on the mass of the object and the amount of force applied (F=maF = maF=ma).
  • Third Law (Action and Reaction) : For every action, there is an equal and opposite reaction.
  • Kinetic Energy : The energy an object has due to its motion (e.g., a moving car).
  • Potential Energy : The energy stored in an object due to its position or state (e.g., a ball at the top of a hill).
  • The product of an object’s mass and its velocity (e.g., a speeding bullet has high momentum).
  • The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it.
  • Gravity : The force of attraction between masses (e.g., objects falling to the ground).
  • Friction : The resistive force that opposes the relative motion of two surfaces in contact (e.g., a sled slowing down on snow).
  • Air Resistance : The frictional force air exerts against a moving object (e.g., slowing down a falling leaf).

FAQ’s

What is uniform motion.

Uniform motion occurs when an object covers equal distances in equal intervals of time.

What is non-uniform motion?

Non-uniform motion occurs when an object covers unequal distances in equal intervals of time.

What is velocity?

Velocity is the speed of an object in a specific direction.

What is the acceleration due to gravity on Earth?

Acceleration is the rate of change of velocity with time.

What is the difference between speed and velocity?

Speed is the rate of distance covered, while velocity includes both speed and direction.

What is deceleration?

Deceleration is negative acceleration, indicating a decrease in velocity.

What is the formula for speed?

Speed is calculated by dividing distance by time (Speed = Distance/Time).

What is displacement?

Displacement is the shortest distance from the initial to the final position, considering direction.

What is the difference between distance and displacement?

Distance is the total path covered, while displacement is the straight-line distance between start and end points.

What is circular motion?

Circular motion is when an object moves along a circular path, maintaining a constant distance from a central point.

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  • Types of Motion

Is it the trees or the train that’s moving. This question might wonder you every time you travel by train. Motion means movement. Everything that moves is said to be in motion, the speed s may be different though. In the chapter below, we will learn Motion and measurement. We will also see ways to differentiate between the different types of motions.

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What is motion.

You see objects moving around you. From cars, cycles to humans, mosquitoes and animals. How do you decide that an object or body is moving? What is the motion of an object? An object is moving when you see a change in its position with time. For example, when you see an ant change its position,  you come to the conclusion that it is in motion.

But there may be some things which change position yet seem not to move, like the Earth. As a result, we define motion as the change in position of an object with respect to a given position.

Browse more Topics under Motion And Measurement Of Distances

  • Evolution of Transport and Measurement of Distance

Types of Motions

The motion of an object shows its changing position, as discussed earlier. But varying objects show varying types of motion. Like for example, a fan is said to be in motion though it is static in its place or a hanging clock that shows motion though it is hanging in its position. We say that motion is mainly of three types: Rectilinear Motion, Circular Motion and Periodic Motion.

Motion and measurement

Rectilinear Motion

In a rectilinear motion, all the objects move along a single line. Some common examples of rectilinear motion are marching soldiers, moving cars, and moving animals. The common thing in all these examples is that they move in a single line.

types of motion essay

Circular Motion

Have you noticed the motion of a fan? Some objects are moving even though they are fixed at some position. Here the fan undergoes circular motion. In the circular motion , the objects follow a circular path of motion without changing their position. It is the circular movement of fan that results in cool air. Some more examples of circular motion are the motion of a Ferry wheel, satellites and rotation of planets around the sun.

types of motion essay

Periodic Motion

Have you ever seen a clock’s pendulum? It repeats its movement after a specific time. Physically the pendulum isn’t moving. It is fixed to some point, yet it shows motion. This kind of motion that repeats after a specific period of time is known as periodic motion. In the periodic motion , the movement made by these objects is called oscillation .

Since it repeats after a fixed period of time, it is named so!  Clocks and table fans are the most common examples. Some other examples of the periodic motion are a child’s motion on swings, the motion of the earth around the Sun, the motion of the moon around the earth.

types of motion essay

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The world around us is moving. Everything that we see is showing some kind of motion. Can you now chalk out a few examples that show all or at least more than one type of motion?

Solved Examples for You

Question: The motion of train and car belongs to:

  •  Translatory motion
  •  Rotatory motion
  •  To and fro motion
  • Spin motion

Solution: Option A. Trains and cars normally move along straight tracks and roads. So their motion is mostly translatory motion. Unless the track or the road is a perfect circle, the motion is not rotatory or to and fro. Thus our answer is the translatory motion.

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  • Introduction To Motion
  • Motion In Physics

Motion in Physics

The concept of motion in physics is one of the important topics in Classical Mechanics. Did you know that everything in the universe is always moving? Even if you are completely still, you still belong to the earth which is continuously moving about its axis and around the sun. Motion means a change in the position of an object with reference to time.

Motion In Physics

What Is Motion in Physics?

In physics, motion is the change in position of an object with respect to its surroundings in a given interval of time. The motion of an object with some mass can be described in terms of the following:

  • Displacement
  • Acceleration

Watch the video and learn more about laws of motion

types of motion essay

Types of Motion in Physics

The motion of an object depends on the type of force acting on the body. Examples of different kinds of motion are given below.

  • Translational  – It is the type, where an object moves along a path in any of the three dimensions.
  • Rotational  – It is the type, where an object moves along a circular path about a fixed axis.
  • Linear  – It is a type of translational motion where the body moves in a single direction along a single dimension.
  • Periodic  – It is the type of motion that repeats itself after certain intervals of time
  • Simple Harmonic  – It is the type of motion like that of a simple pendulum where a restoring force acts in the direction opposite to the direction of motion of the object. This restoring force is proportional to the displacement of the object from the mean position.
  • Projectile – It is the type of motion which has a horizontal displacement as well as vertical displacement.
  • Oscillatory  – It is the type of motion which is repetitive in nature within a time frame. If it is mechanical it is called vibration.

Read More: Laws of Motion

Laws of Motion

Newton’s Laws of Motion laid the foundation for classical mechanics today. Although subject to minor limitations, these laws of motion are valid everywhere and are therefore used. The laws are given as stated below in a brief description

  • First Law : Any object will remain in its existing state of motion or rest unless a net external force acts on it.
  • Second Law : If an object has a certain mass, the greater the mass of this object, the greater will the force required to be to accelerate the object. It is represented by the equation F = ma, where ‘F’ is the force on the object, ‘m’ is the mass of the object and ‘a’ is the acceleration of the object.
  • Third Law : For every action, there is an equal and opposite reaction.

The below video provides the Top 10 NTSE Important Questions on Motion Class 9

types of motion essay

Frequently Asked Questions – FAQs

What is periodic motion, what is rotational motion, what is newton’s first law of motion, state newton’s third law of motion., what is oscillatory motion, the below video provides the complete quiz of the chapter motion class 9.

types of motion essay

Motion is an important concept in Physics which can be better understood by applying conceptual knowledge to solve problems. Stay tuned with BYJU’S and learn various interesting physics topics with the help of engaging video lessons.

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What Are Newton's Laws of Motion?

Newton's First, Second and Third Laws of Motion

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Newton's Laws of Motion help us understand how objects behave when standing still; when moving, and when forces act upon them. There are three laws of motion. Here is a description of Sir Isaac Newton's Laws of Motion and a summary of what they mean.

Newton's First Law of Motion

Newton's First Law of Motion states that an object in motion tends to stay in motion unless an external force acts upon it. Similarly, if the object is at rest, it will remain unless an unbalanced force acts upon it. Newton's First Law of Motion is also known as the Law of Inertia .

What Newton's First Law is saying is that objects behave predictably. If a ball is sitting on your table, it isn't going to start rolling or fall off the table unless a force acts upon it to cause it to do so. Moving objects don't change their direction unless a force causes them to move from their path.

As you know, if you slide a block across a table, it eventually stops rather than continuing forever. This is because the frictional force opposes the continued movement. If you throw a ball out in space, there is much less resistance. The ball will continue onward for a much greater distance.

Newton's Second Law of Motion

Newton's Second Law of Motion states that when a force acts on an object, it will cause the object to accelerate. The larger the object's mass, the greater the force will need to be to cause it to accelerate. This Law may be written as force = mass x acceleration or:

F = m * a

Another way to state the Second Law is to say it takes more force to move a heavy object than it does to move a light object. Simple, right? The law also explains deceleration or slowing down. You can think of deceleration as acceleration with a negative sign on it. For example, a ball rolling down a hill moves faster or accelerates as gravity acts on it in the same direction as the motion (acceleration is positive). If a ball is rolled up a hill, the force of gravity acts on it in the opposite direction of the motion (acceleration is negative or the ball decelerates).

Newton's Third Law of Motion

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.

This means that pushing on an object causes that object to push back against you, the same amount but in the opposite direction. For example, when you are standing on the ground, you are pushing down on the Earth with the same magnitude of force it is pushing back up at you.

History of Newton's Laws of Motion

Sir Isaac Newton introduced the three Newton's laws of motion in 1687 in his book entitled "Philosophiae Naturalis Principia Mathematica" (or simply "The Principia"). The same book also discussed the theory of gravity . This one volume described the main rules still used in classical mechanics today.

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What is Motion and Types of Motion

February 17, 2023 by Veerendra

What is Motion

When a body does not change its position with time, we can say that the body is at rest, while if a body changes its position with time, it is said to be in motion .

Analysing Linear Motion

Analysing Linear Motion 1

  • Linear motion is motion in a straight line.
  • Non-linear motion is motion that is not in a straight line.
  • When analysing linear and non-linear motion, distance, displacement, speed, velocity, acceleration and deceleration are some commonly encountered physical quantities.

Terms Used To Define Motion 

  • Distance and Displacement
  • Speed and Velocity
  • Acceleration

An object is said to be a point object if it changes its position by distances which are much greater than its size. A point or some stationary object with respect to which a body continuously changes its position in the state of motion is known as origin or reference point.

motion

Types Of Motion

There are different types of motion: translational, rotational, periodic, and non periodic motion.

Translational Motion A type of motion in which all parts of an object move the same distance in a given time is called translational motion. Examples are vehicles moving on a road, a child going down a bird flying in the sky. Translational motion can be of two types, rectilinear and curvilinear. Table shows the differences between rectilinear and curvilinear motions.

1. When an object in translational motion moves in a straight line, it is said to be in rectilinear motion.1. When an object in translational motion moves along a curved path, it is said to be in curvilinear motion.
2. Examples are a car moving on a straight road and a train moving on a straight track.2. Examples are a stone thrown up in the air at an angle and a car taking a turn.

translational-motion-Example

Rotational Motion When an object moves about an axis and different parts of it move by different distances in a given interval of time, it is said to be in rotational motion. Examples of objects undergoing rotational motion are blades of a rotating fan, merry-go-round, blades of a windmill. When an object undergoes rotational motion, all its parts do not move the same distance in a given interval of time. For example, the outer portion of the blades of a windmill moves much more than the portion closer to the centre.

rotational-motion

Periodic Motion A type of motion that repeats itself after equal intervals of time is called periodic motion. Examples of objects undergoing periodic motion are the to and fro motion of a pendulum, the Earth (rotating on its axis), the hands of a clock, the blades of a rotating electric fan, and the plucked string of a guitar.

periodic-motion-Example

Non-periodic Motion A motion that does not repeat itself at regular intervals or a motion that does not repeat itself at all is called non-periodic motion. Examples of non-periodic motion are a car moving on a road, a bird gliding across the sky, and children playing in a park. In everyday life, we observe more than one type of motion, like

  • Birds gliding across the sky (translational and non periodic).
  • Rotation of the Earth on its axis (rotational and periodic).

non-periodic-motion-Example

According to Directions

  • One dimensional motion is the motion of a particle moving along a straight line.
  • Two dimensional motion A particle moving along a curved path in a plane has 2-dimensional motion.
  • Three dimensional motion Particle moving randomly in space has 3-dimensional motion.

According to State of Motion

  • Uniform Motion:  A body is said to be in a state of uniform motion if it travels equal distances in equal intervals of time. If the time distance graph is a straight line the motion is said to be uniform motion.
  • Non-uniform motion:  A body has a non-uniform motion if it travels unequal distances in equal intervals of time. Ex. a freely falling body. Time – distance graph for a body with non-uniform motion is a curved line.

Analysing Motion Graphs

Analysing Motion Graphs 1

  • Figure shows a tortoise moving at a slow and steady speed while a hare was sleeping soundly from the time t = 0 to 8 s.

Analysing Motion Graphs 2

Velocity -Time graphs:

Analysing Motion Graphs 5

  • The gradients of the s-t graphs for the tortoise and hare are 0.25 m s -1  and 0 m s -1  respectively.

Analysing Motion Graphs 6

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Home — Essay Samples — Science — Physics — Newton'S Laws of Motion

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Essays on Newton's Laws of Motion

Sir Isaac Newton's Laws of Motion are fundamental principles in the field of physics, providing the basis for understanding the behavior of objects in motion. These laws have been essential in shaping our understanding of the physical world and are a cornerstone of modern physics. As such, there are numerous essay topics that can be explored within the realm of Newton's Laws of Motion, offering students the opportunity to delve into the intricacies of these fundamental principles.

The Importance of the Topic

Understanding Newton's Laws of Motion is crucial for anyone studying physics or engineering. These laws govern the behavior of objects in motion and provide a framework for analyzing and predicting the motion of objects. By studying these laws, students can gain a deeper understanding of how the physical world works and apply this knowledge to real-world situations.

Additionally, exploring essay topics related to Newton's Laws of Motion can help students develop critical thinking and problem-solving skills. By delving into these complex principles, students can learn how to analyze and interpret scientific concepts, as well as communicate their findings effectively through writing.

Advice on Choosing a Topic

When choosing a topic for an essay on Newton's Laws of Motion, it is important to consider your interests and the specific aspects of the laws that you find most intriguing. Consider exploring topics that relate to real-world applications of the laws, historical context, or modern advancements in the field of physics. Additionally, consider topics that allow for in-depth research and analysis, as this will provide the opportunity to delve into the complexities of Newton's Laws of Motion.

It may also be beneficial to consider the audience for your essay and choose a topic that will engage and educate your readers. By selecting a topic that is relevant and interesting, you can ensure that your essay will captivate the attention of your audience and effectively convey the significance of Newton's Laws of Motion.

Newton's Laws of Motion offer a wealth of opportunities for exploration and analysis through essay topics. By delving into these fundamental principles, students can gain a deeper understanding of the physical world and develop critical thinking and problem-solving skills. When choosing a topic for an essay on Newton's Laws of Motion, it is important to consider your interests, the relevance of the topic, and the potential for in-depth research and analysis. By selecting a compelling topic, students can effectively convey the significance of Newton's Laws of Motion and engage their audience in the complexities of these fundamental principles.

An Overview of Newton’s Law of Motion and Its Role in Our Lives

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Newton’s Second Law of Motion: Experiment Report

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If you had to think consciously in order to move your body, you would be severely disabled. Even walking, which we consider to be no great feat, requires an intricate series of motions your cerebrum would be utterly incapable of coordinating. The task of putting one foot in front of the other is controlled by the more primitive parts of your brain, the ones that have not changed much since the mammals and reptiles went their separate evolutionary ways. The thinking part of your brain limits itself to general directives such as “walk faster,” or “don’t step on her toes,” rather than micromanaging every contraction and relaxation of the hundred or so muscles of your hips, legs, and feet.

Physics is all about the conscious understanding of motion, but we are obviously not immediately prepared to understand the most complicated types of motion. Instead, we will use the divide-and-conquer technique. We will first classify the various types of motion, and then begin our campaign with an attack on the simplest cases. To make it clear what we are and are not ready to consider, we need to examine and define carefully what types of motion can exist.

Rigid-body motion distinguished from motion that changes an object’s shape

Nobody, with the possible exception of Fred Astaire, can simply glide forward without bending their joints. Walking is thus an example in which there is both a general motion of the whole object and a change in the shape of the object. Another example is the motion of a jiggling water balloon as it flies through the air. We are not presently attempting a mathematical description of the way in which the shape of an object changes. Motion without a change in shape is called rigid-body motion (the word “body” is often used in physics as a synonym for “object”).

Center-of-mass motion as opposed to rotation

A ballerina leaps into the air and spins around once before landing. We feel intuitively that her rigid-body motion while her feet are off the ground consists of two kinds of motion going on simultaneously: a rotation and a motion of her body as a whole through space, along an arc. It is not immediately obvious, however, what is the most useful way to define the distinction between rotation and motion through space. Imagine you attempt to balance a chair and it falls over. One person might say that the only motion was a rotation about the chair’s point of contact with the floor, but another might say there was both rotation and motion down and to the side.

It turns out there is one particularly natural and useful way to make a clear definition, but it requires a brief digression. Every object has a balance point, referred to in physics as the center of mass. For a two-dimensional object such as a cardboard cutout, the center of mass is the point at which you could hang the object from a string and make it balance. In the case of the ballerina (who is likely to be three-dimensional unless her diet is particularly severe), it might be a point either inside or outside her body, depending on how she holds her arms. Even if it is not practical to attach a string to the balance point itself, the center of mass can be defined.

Why is the center of mass concept relevant to the question of classifying rotational motion as opposed to motion through space? It turns out that the motion of an object’s center of mass is nearly always far simpler than the motion of any other part of the object. The ballerina’s body is a large object with a complex shape. We might expect that her motion would be much more complicated than the motion of a small, simply-shaped object, say a marble, thrown up at the same angle as the angle at which she leapt. But it turns out that the motion of the ballerina’s center of mass is exactly the same as the motion of the marble. That is, the motion of the center of mass is the same as the motion the ballerina would have if all her mass was concentrated at a point. By restricting our attention to the motion of the center of mass, we can therefore simplify things greatly.

We can now replace the ambiguous idea of “motion as a whole through space” with the more useful and better defined concept of “center-of-mass motion.” The motion of any rigid body can be cleanly split into rotation and center-of-mass motion. By this definition, the tipping chair does have both rotational and center-of-mass motion. Concentrating on the center of mass motion allows us to make a simplified model of the motion, as if a complicated object like a human body was just a marble or a point-like particle. Science really never deals with reality; it deals with models of reality.

Note that the word “center” in “center of mass” is not meant to imply that the center of mass must lie at the geometrical center of an object. A car wheel that has not been balanced properly has a center of mass that does not coincide with its geometrical center. An object such as the human body does not even have an obvious geometrical center.

It can be helpful to think of the center of mass as the average location of all the mass in the object. With this interpretation, we can see for example that raising your arms above your head raises your center of mass, since the higher position of the arms’ mass raises the average. jete-illusion

Ballerinas and professional basketball players can create an illusion of flying horizontally through the air because our brains intuitively expect them to have rigid-body motion, but the body does not stay rigid while executing a grand jete or a slam dunk. The legs are low at the beginning and end of the jump, but come up higher at the middle. Regardless of what the limbs do, the center of mass will follow the same arc, but the low position of the legs at the beginning and end means the torso is higher compared to the center of mass, while in the middle of the jump it is lower compared to the center of mass. Our eye follows the motion of the torso and tries to interpret it as the center-of-mass motion of a rigid body. But since the torso follows a path flatter than we expect, this attempted interpretation fails, and we experience an illusion that the person is flying horizontally.

Center-of-mass motion in one dimension

In addition, there are cases in which the center of mass moves along a straight line, such as objects falling straight down, or a car that speeds up and slows down but does not turn.

Note that even though we are not explicitly studying the more complex aspects of motion, we can still analyze the center-of-mass motion while ignoring other types of motion that might be occurring simultaneously. For instance, if a cat is falling out of a tree and is initially upside-down, it goes through a series of contortions that bring its feet under it. This is definitely not an example of rigid-body motion, but we can still analyze the motion of the cat’s center of mass just as we would for a dropping rock.

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4.4 Newton's Third Law of Motion

Section learning objectives.

By the end of this section, you will be able to do the following:

  • Describe Newton’s third law, both verbally and mathematically
  • Use Newton’s third law to solve problems

Teacher Support

The learning objectives in this section will help your students master the following standards:

  • (D) calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects.

Section Key Terms

Newton’s third law of motion normal force tension thrust

Describing Newton’s Third Law of Motion

[BL] [OL] Review Newton’s first and second laws.

[AL] Start a discussion about action and reaction by giving examples. Introduce the concepts of systems and systems of interest. Explain how forces can be classified as internal or external to the system of interest. Give examples of systems. Ask students which forces are internal and which are external in each scenario.

If you have ever stubbed your toe, you have noticed that although your toe initiates the impact, the surface that you stub it on exerts a force back on your toe. Although the first thought that crosses your mind is probably “ouch, that hurt” rather than “this is a great example of Newton’s third law,” both statements are true.

This is exactly what happens whenever one object exerts a force on another—each object experiences a force that is the same strength as the force acting on the other object but that acts in the opposite direction. Everyday experiences, such as stubbing a toe or throwing a ball, are all perfect examples of Newton’s third law in action.

Newton’s third law of motion states that whenever a first object exerts a force on a second object, the first object experiences a force equal in magnitude but opposite in direction to the force that it exerts.

Newton’s third law of motion tells us that forces always occur in pairs, and one object cannot exert a force on another without experiencing the same strength force in return. We sometimes refer to these force pairs as action-reaction pairs, where the force exerted is the action, and the force experienced in return is the reaction (although which is which depends on your point of view).

Newton’s third law is useful for figuring out which forces are external to a system. Recall that identifying external forces is important when setting up a problem, because the external forces must be added together to find the net force .

We can see Newton’s third law at work by looking at how people move about. Consider a swimmer pushing off from the side of a pool, as illustrated in Figure 4.8 . She pushes against the pool wall with her feet and accelerates in the direction opposite to her push. The wall has thus exerted on the swimmer a force of equal magnitude but in the direction opposite that of her push. You might think that two forces of equal magnitude but that act in opposite directions would cancel, but they do not because they act on different systems.

In this case, there are two different systems that we could choose to investigate: the swimmer or the wall. If we choose the swimmer to be the system of interest, as in the figure, then F wall on feet F wall on feet is an external force on the swimmer and affects her motion. Because acceleration is in the same direction as the net external force , the swimmer moves in the direction of F wall on feet . F wall on feet . Because the swimmer is our system (or object of interest) and not the wall, we do not need to consider the force F feet on wall F feet on wall because it originates from the swimmer rather than acting on the swimmer. Therefore, F feet on wall F feet on wall does not directly affect the motion of the system and does not cancel F wall on feet . F wall on feet . Note that the swimmer pushes in the direction opposite to the direction in which she wants to move.

Other examples of Newton’s third law are easy to find. As a teacher paces in front of a whiteboard, he exerts a force backward on the floor. The floor exerts a reaction force in the forward direction on the teacher that causes him to accelerate forward. Similarly, a car accelerates because the ground pushes forward on the car's wheels in reaction to the car's wheels pushing backward on the ground. You can see evidence of the wheels pushing backward when tires spin on a gravel road and throw rocks backward.

Another example is the force of a baseball as it makes contact with the bat. Helicopters create lift by pushing air down, creating an upward reaction force. Birds fly by exerting force on air in the direction opposite that in which they wish to fly. For example, the wings of a bird force air downward and backward in order to get lift and move forward. An octopus propels itself forward in the water by ejecting water backward through a funnel in its body, which is similar to how a jet ski is propelled. In these examples, the octopus or jet ski push the water backward, and the water, in turn, pushes the octopus or jet ski forward.

Applying Newton’s Third Law

[BL] Review the concept of weight as a force.

[OL] Ask students what happens when an object is dropped from a height. Why does it stop when it hits the ground? Introduce the term normal force.

Teacher Demonstration

[BL] [OL] [AL] Demonstrate the concept of tension by using physical objects. Suspend an object such as an eraser from a peg by using a rubber band. Hang another rubber band beside the first but with no object attached. Ask students what the difference is between the two. What are the forces acting on the first peg? Explain how the rubber band (i.e., the connector) transmits force. Now ask students what the direction of the external forces acting on the connectoris. Also, ask what internal forces are acting on the connector. If you remove the eraser, in which direction will the rubber band move? This is the direction of the force the rubber band applied to the eraser.

Forces are classified and given names based on their source, how they are transmitted, or their effects. In previous sections, we discussed the forces called push , weight , and friction . In this section, applying Newton’s third law of motion will allow us to explore three more forces: the normal force , tension , and thrust . However, because we haven’t yet covered vectors in depth, we’ll only consider one-dimensional situations in this chapter. Another chapter will consider forces acting in two dimensions.

The gravitational force (or weight ) acts on objects at all times and everywhere on Earth. We know from Newton’s second law that a net force produces an acceleration; so, why is everything not in a constant state of freefall toward the center of Earth? The answer is the normal force. The normal force is the outward force that a surface applies to an object perpendicular to the surface, and it prevents the object from penetrating it. In the case of an object at rest on a horizontal surface, it is the force needed to support the weight of that object. If an object on a flat surface is not accelerating, the net external force is zero, and the normal force has the same magnitude as the weight of the system but acts in the opposite direction. In equation form, we write that

Note that this equation is only true for a horizontal surface.

The word tension comes from the Latin word meaning to stretch . Tension is the force along the length of a flexible connector, such as a string, rope, chain, or cable. Regardless of the type of connector attached to the object of interest, one must remember that the connector can only pull (or exert tension ) in the direction parallel to its length. Tension is a pull that acts parallel to the connector, and that acts in opposite directions at the two ends of the connector. This is possible because a flexible connector is simply a long series of action-reaction forces, except at the two ends where outside objects provide one member of the action-reaction forces.

Consider a person holding a mass on a rope, as shown in Figure 4.9 .

Tension in the rope must equal the weight of the supported mass, as we can prove by using Newton’s second law. If the 5.00 kg mass in the figure is stationary, then its acceleration is zero, so F net = 0. F net = 0. The only external forces acting on the mass are its weight W and the tension T supplied by the rope. Summing the external forces to find the net force, we obtain

where T and W are the magnitudes of the tension and weight, respectively, and their signs indicate direction, with up being positive. By substituting m g for F net and rearranging the equation, the tension equals the weight of the supported mass, just as you would expect

For a 5.00-kg mass (neglecting the mass of the rope), we see that

Another example of Newton’s third law in action is thrust. Rockets move forward by expelling gas backward at a high velocity. This means that the rocket exerts a large force backward on the gas in the rocket combustion chamber, and the gas, in turn, exerts a large force forward on the rocket in response. This reaction force is called thrust .

Tips For Success

A common misconception is that rockets propel themselves by pushing on the ground or on the air behind them. They actually work better in a vacuum, where they can expel exhaust gases more easily.

Links To Physics

Math: problem-solving strategy for newton’s laws of motion.

The basics of problem solving, presented earlier in this text, are followed here with specific strategies for applying Newton’s laws of motion. These techniques also reinforce concepts that are useful in many other areas of physics.

First, identify the physical principles involved. If the problem involves forces, then Newton’s laws of motion are involved, and it is important to draw a careful sketch of the situation. An example of a sketch is shown in Figure 4.10 . Next, as in Figure 4.10 , use vectors to represent all forces. Label the forces carefully, and make sure that their lengths are proportional to the magnitude of the forces and that the arrows point in the direction in which the forces act.

Next, make a list of knowns and unknowns and assign variable names to the quantities given in the problem. Figure out which variables need to be calculated; these are the unknowns. Now carefully define the system: which objects are of interest for the problem. This decision is important, because Newton’s second law involves only external forces. Once the system is identified, it’s possible to see which forces are external and which are internal (see Figure 4.10 ).

If the system acts on an object outside the system, then you know that the outside object exerts a force of equal magnitude but in the opposite direction on the system.

A diagram showing the system of interest and all the external forces acting on it is called a free-body diagram. Only external forces are shown on free-body diagrams, not acceleration or velocity. Figure 4.10 shows a free-body diagram for the system of interest.

After drawing a free-body diagram, apply Newton’s second law to solve the problem. This is done in Figure 4.10 for the case of Tarzan hanging from a vine. When external forces are clearly identified in the free-body diagram, translate the forces into equation form and solve for the unknowns. Note that forces acting in opposite directions have opposite signs. By convention, forces acting downward or to the left are usually negative.

Grasp Check

If a problem has more than one system of interest, more than one free-body diagram is required to describe the external forces acting on the different systems.

Watch Physics

Newton’s third law of motion.

This video explains Newton’s third law of motion through examples involving push, normal force, and thrust (the force that propels a rocket or a jet).

If the astronaut in the video wanted to move upward, in which direction should he throw the object? Why?

  • He should throw the object upward because according to Newton’s third law, the object will then exert a force on him in the same direction (i.e., upward).
  • He should throw the object upward because according to Newton’s third law, the object will then exert a force on him in the opposite direction (i.e., downward).
  • He should throw the object downward because according to Newton’s third law, the object will then exert a force on him in the opposite direction (i.e., upward).
  • He should throw the object downward because according to Newton’s third law, the object will then exert a force on him in the same direction (i.e., downward).

Worked Example

An accelerating equipment cart.

A physics teacher pushes a cart of demonstration equipment to a classroom, as in Figure 4.11 . Her mass is 65.0 kg, the cart’s mass is 12.0 kg, and the equipment’s mass is 7.0 kg. To push the cart forward, the teacher’s foot applies a force of 150 N in the opposite direction (backward) on the floor. Calculate the acceleration produced by the teacher. The force of friction, which opposes the motion, is 24.0 N.

Because they accelerate together, we define the system to be the teacher, the cart, and the equipment. The teacher pushes backward with a force F foot F foot of 150 N. According to Newton’s third law, the floor exerts a forward force F floor F floor of 150 N on the system. Because all motion is horizontal, we can assume that no net force acts in the vertical direction, and the problem becomes one dimensional. As noted in the figure, the friction f opposes the motion and therefore acts opposite the direction of F floor . F floor .

We should not include the forces F teacher F teacher , F cart F cart , or F foot F foot because these are exerted by the system, not on the system. We find the net external force by adding together the external forces acting on the system (see the free-body diagram in the figure) and then use Newton’s second law to find the acceleration.

Newton’s second law is

The net external force on the system is the sum of the external forces: the force of the floor acting on the teacher, cart, and equipment (in the horizontal direction) and the force of friction. Because friction acts in the opposite direction, we assign it a negative value. Thus, for the net force, we obtain

The mass of the system is the sum of the mass of the teacher, cart, and equipment.

Insert these values of net F and m into Newton’s second law to obtain the acceleration of the system.

None of the forces between components of the system, such as between the teacher’s hands and the cart, contribute to the net external force because they are internal to the system. Another way to look at this is to note that the forces between components of a system cancel because they are equal in magnitude and opposite in direction. For example, the force exerted by the teacher on the cart is of equal magnitude but in the opposite direction of the force exerted by the cart on the teacher. In this case, both forces act on the same system, so they cancel. Defining the system was crucial to solving this problem.

Practice Problems

What is the equation for the normal force for a body with mass m that is at rest on a horizontal surface?

An object with mass m is at rest on the floor. What is the magnitude and direction of the normal force acting on it?

  • N = mv in upward direction
  • N = mg in upward direction
  • N = mv in downward direction
  • N = mg in downward direction

Check Your Understanding

Use the questions in Check Your Understanding to assess whether students have mastered the learning objectives of this section. If students are struggling with a specific objective, the Check Your Understanding assessment will help identify which objective is causing the problem and direct students to the relevant content.

What is Newton’s third law of motion?

  • Whenever a first body exerts a force on a second body, the first body experiences a force that is twice the magnitude and acts in the direction of the applied force.
  • Whenever a first body exerts a force on a second body, the first body experiences a force that is equal in magnitude and acts in the direction of the applied force.
  • Whenever a first body exerts a force on a second body, the first body experiences a force that is twice the magnitude but acts in the direction opposite the direction of the applied force.
  • Whenever a first body exerts a force on a second body, the first body experiences a force that is equal in magnitude but acts in the direction opposite the direction of the applied force.

Considering Newton’s third law, why don’t two equal and opposite forces cancel out each other?

  • Because the two forces act in the same direction
  • Because the two forces have different magnitudes
  • Because the two forces act on different systems
  • Because the two forces act in perpendicular directions

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-physics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/physics/pages/1-introduction
  • Authors: Paul Peter Urone, Roger Hinrichs
  • Publisher/website: OpenStax
  • Book title: Physics
  • Publication date: Mar 26, 2020
  • Location: Houston, Texas
  • Book URL: https://openstax.org/books/physics/pages/1-introduction
  • Section URL: https://openstax.org/books/physics/pages/4-4-newtons-third-law-of-motion

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Motion Graphs: Explanation, Review, and Examples

  • The Albert Team
  • Last Updated On: March 31, 2022

Review motion graphs, including position-time graphs and velocity-time graphs, with Albert

When trying to explain how things move, physicists don’t just use equations – they also use graphs! Motion graphs allow scientists to learn a lot about an object’s motion with just a quick glance. This article will cover the basics for interpreting motion graphs including different types of graphs, how to read them, and how they relate to each other. Interpreting motion graphs, such as position vs time graphs and velocity vs time graphs, requires knowledge of how to find slope. If you need a review or find yourself having trouble, this article should be able to help.

What We Review

Types of Motion Graphs

There are three types of motion graphs that you will come across in the average high school physics course – position vs time graphs, velocity vs time graphs, and acceleration vs time graphs. An example of each one can be seen below.

The position vs time graph (on the left) shows how far away something is relative to an observer.

The velocity vs time graph (in the middle) shows you how quickly something is moving, again relative to an observer.

Finally, the acceleration vs time graph (on the right) shows how quickly something is speeding up or slowing down, relative to an observer.

Motion graphs include position vs time graphs, velocity vs time graphs, and acceleration vs time graphs.

Because all of these are visual representations of a movement, it is important to know your frame of reference. We learned in our introduction to kinematics that two people can observe the same event but describe it differently depending upon where they stand. If this or anything about the position, velocity, and/or acceleration is still a bit confusing, revisit our kinematics post and our acceleration post before moving on.

Describing Motion with Position vs Time Graph s

A position vs time graph for an object moving steadily away from an observer.

We typically start with position-time graphs when learning how to interpret motion graphs – generally because they’re the easiest to try to picture. Let’s look at the position vs time graph from above. We see that our vertical axis is Position (in meters) and that our horizontal axis is Time (in seconds). This means we know how far away an object has moved from our observer at any given time. This particular graph shows an object moving steadily away from our observer.

Position vs Time Graph for Multi-Stage Motion

Let’s consider the graph and images below. We are still considering a position vs time graph, but this time we are looking at motion that changes. The car begins by moving 5 meters away from the observer in the first 5 seconds. After that, the car remains stopped 5 meters away from the observer for another 5 seconds. Finally, the car turns around and moves for 5 seconds back to its original position, 0 meters from the observer.

A position vs time graph for a car moving away from the observing, stopping, and then returning.

There are two key points that we can take from the example above. The first is that our position vs time graph shows how far away we are at any given time and nothing else. It cannot tell us distance or displacement – we would have to do a little mathematics to find those out. The second is that the change in position is not always positive. Here, we’ve defined moving to the right as positive. So, in the beginning, when the car was moving to the right, its position increased. In the end, when it moved back to the left, it was moving in the negative direction.

Position vs Time Graph for Passing an Observer

This implies that the position could, potentially, go below the x-axis. Let’s look at an example combining these two points in practice.

A position vs time graph for an object moving past an observer in the negative direction. The graph has a negative slope.

This time, our car started to the right, and drove straight past our observer to the left. At t=0\text{ s} , the car was 10\text{ m} to the right of our observer, so its position was x=10\text{ m} . As it passed the observer, its position was x=0\text{ m} at t=5\text{ s} . The car then ended its journey 10\text{ m} to our observers left at t=10\text{ s} so that its final position was x=-10\text{ m} .

Finding Distance and Displacement from a Position vs Time Graph

Example 1: constant position vs time graph.

We’ll continue working from the graph above as we have already pulled the important values from it. Because we have a simple, straight line we only need the values from the very beginning and very end of the car’s journey, which we already pulled out above:

  • t_{1}=0\text{ s}
  • x_{1}=10\text{ m}
  • t_{2}=10\text{ s}
  • x_{2}=-10\text{ m}

Finding Distance From A Position-Time Graph

As we learned from our introduction to kinematics lesson, we know that the equation for distance is:


d_{T}=d_{1}+d_{2}

The problem here is that we didn’t pull out any d values from our position vs time graph, only x values. We can still use those, though. In general, if you take the absolute value of an x value, it can be thought of as a d value and plugged into our distance equation. So the d values we’ll be using are:

  • d_{1}=\lvert x_{1} \rvert =\lvert 10\text{ m} \rvert = 10\text{ m}
  • d_{2}=\lvert x_{2} \rvert =\lvert -10\text{ m} \rvert = 10\text{ m}

Now we can plug these values into our equation and solve for our distance.

Finding Displacement From A Position vs Time Graph

Our equation for displacement is:


\Delta x=x_{f}-x_{i}

In this case, we will be using x_{2} as x_{f} and x_{1} as x_{i} as they represent the end and beginning of our movements, respectively. When we plug in our values, we find:

In this case, the negative sign makes sense as our line is moving down the graph and the car moved from right to left, which we had previously defined as positive to negative.

Example 2: Changing Position vs Time Graph

Now that we know the basics of finding distance and displacement from a position vs time graph, let’s get a bit more in-depth. We’ll return to the graph about the car that moved forward, stopped, and then turned around and returned to its original position. The graph has been copied below for convenience.

A position vs time graph for an object moving away from the observer, stopping, then turn around and returning to the observer.

How to Find Distance From A Position vs Time Graph

Finding distance from these graphs can get a bit complex as you’ll need to find several different values. If you’ll notice, the slope of our graph changes regularly – the line seems to turn. Each segment with a unique slope requires our attention. So, we’ll need to look at t=0\text{ s} through t=5\text{ s} ,  t=5\text{ s} through  t=10\text{ s} , and  t=10\text{ s} through  t=15\text{ s} .

We’ll want to look at the position value on the left and right of each side of those segments and find the absolute value of the delta between those values. These will serve as the d values that we will plug into our distance equation.

  • d_{1}=\lvert 5\text{ m}-0\text{ m} \rvert =5\text{ m}
  • d_{2}=\lvert 5\text{ m}-5\text{ m} \rvert =0\text{ m}
  • d_{3}=\lvert 0\text{ m}-5\text{ m} \rvert =5\text{ m}

We can now plug all of these values into our equation and solve for distance.

How to Find Displacement From A Position vs Time Graph

Finding displacement from a graph that changes how it’s moving is a bit easier than finding the distance. Because displacement only concerns the distance between the starting and ending positions of an object’s motion, we only need to find the position at the rightmost point on the graph ( t=15\text{ s} ) and the leftmost point on the graph ( t=0\text{ s} ). The positions at these times will serve as our x_{f} and x_{i} values respectively. 

  • x_{f}=0\text{ m}
  • x_{i}=0\text{ m}

Now that we have these values, we can plug them into our displacement formula and solve:

Finding Velocity from a Position vs Time Graph

Now that we know how to find distance and displacement from a position vs time graph, we can start finding another value – velocity. If you think about it, these distances and displacements that we’re finding are occurring over some amount of time (as given by the graph) and all we really need to find velocity is displacement and time. So let’s start with a simple graph – the one of an object moving steadily away.

types of motion essay

The displacement for the movement depicted by this graph would be \Delta x=25\text{ m}-0\text{ m}=25\text{ m} and because our time here moves from t=0\text{ s} to t=5\text{ s} , we have a change in time of \Delta t=5\text{ s} . This is enough information for us to solve for the velocity using the equation we learned before:

One very important thing you may notice if you’re savvy with slopes is that the slope of this graph is also equal to 5 . (If you are not particularly savvy with slopes, I would recommend reviewing how to solve for slope as we’ll be relying on that knowledge for most of what remains of this post.) This similarity is no mere coincidence. The velocity of any movement will always be equal to the slope of the position-time graph at that time.

Proving Velocity is the Slope of Position vs Time Graphs

The slope of any given straight line can be found with the equation


m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

Here, m is the slope, y_{2} and y_{1} are two different position values, and x_{2} and x_{1} are the time values corresponding to the two position values.

Let’s begin by selecting two points off of our graph above (being sure to include the units when we do). Let’s take (2\text{ s},10\text{ m}) and (4\text{ s},20\text{ m}) and plug the values in:

This setup of subtracting the rightmost value from the leftmost value should look a bit familiar. Another way to think of it is as taking a final value and subtracting an initial value, much like a delta. In fact, this is equivalent to a change in position over a change in time – the definition of velocity.

Let’s make sure our slope works out to be a velocity value before we jump to any conclusions, though. If the slope of this graph is also the velocity of the same motion, two things need to be true. First, we need a numerical value of 5 . Second, we need our units to be in m/s. Let’s solve the equation above and see what we get.

We have a value that matches the velocity we solved for in both numerical value and physical units. We could have selected any two points on our graph and received the same result. The part of this that truly proves the slope of any position-time graph is the velocity is that the units of our slope work out to be m/s – the units for velocity.

Example 1: Finding Velocity from a Position vs Time Graph

Let’s try finding our velocity again, but using the slope formula. We’ll reuse the graph below that we saw earlier in this article.

We’ll want to begin by selecting the points we want to use. This graph is a straight line which means its slope never changes so it won’t particularly matter what two points we choose. Since we have a point where our x value is zero and a separate point where our y value is zero, we may as well use those to make the mathematics easier. So, the values we’ll be using here are:

  • y_{2}=0\text{ m}
  • y_{1}=10\text{ m}
  • x_{2}=5\text{ s}
  • x_{1}=0\text{ s}

Now, all we need to do is set our velocity equal to our slope, plug in our values, and solve for our velocity:

Here, we get a negative velocity of v=-2\text{ m/s} . If we look at our graph, we see it has a negative slope, so we should have expected this negative velocity from the start. If you ever get a positive when you expected a negative or vice versa, check to make sure you plugged your values into your formula in the correct order. That simple mistake has thrown many scientists off course.

Example 2: Finding Velocity with Changing Motion

Being able to find the velocity of a simple, straight position vs time graph is all well and good, but there will be times when you’ll have to split a graph apart. Let’s revisit the graph below as an example of this.

A position vs time graph for an object moving away from the observer, stopping, then turn around and returning to the observer.

We already said before that we could split this graph up into a few different chunks based on when the slope changes. We know what happens when we have a positive slope and what happens when we have a negative slope, though, so let’s look at just the middle section where it’s flat. Here, the values we can pull from the line segment are:

  • y_{2}=5\text{ m}
  • y_{1}=5\text{ m}
  • x_{1}=10\text{ s}

If we plug these values into our slope formula, we can find that

Since the segment was a flat line with a slope of 0 , the velocity also had to be 0\text{ m/s} . If we recall, this graph depicted a car that moved in the positive direction, stopped and remained motionless, and then moved back in the negative direction. The middle segment of this graph, the one that we looked at, corresponds to when the car was stopped so again. Therefore, it makes sense that we would see a velocity of 0\text{ m/s} .

Describing Motion with Velocity vs Time Graph s

Velocity-time graphs are relatively similar to position-time graphs, and just as important in the study of motion graphs. We still have our time in seconds along the x-axis, but now we have our velocity in meters per second along the y-axis. Let’s consider the velocity-time graph below. 

A velocity vs time graph for an object moving with a constant, positive velocity is a diagonal line.

To find the velocity of an object at any given time here, we simply need to read the value from the graph. There’s no mathematics to do or formulas to use. So, for example, at t=2\text{ s} the velocity is v=4\text{ m/s} because that is the value we read off of the graph. Similarly, the velocity is t=4\text{ s} is v=8\text{ m/s} . The fact that those two values differ and that the slope here is positive tells us that the motion in this graph is an object moving away from an observer and getting faster – like a car leaving a stoplight. We can also show more complicated motions and dip below the x-axis.

Velocity vs Time Graph with a Change in Direction

A velocity vs time graph for an object that changes direction crosses the x-axis.

Let’s imagine a scenario for the graph to the right. We see that the graph starts with the object’s top velocity of v=10\text{ m/s} and then seems to get lower. The object reaches a velocity of v=0\text{ m/s} at t=2.5\text{ s} . While it may make sense to say that the object is now at the same point as the observer, we can’t actually infer that. All we can tell from here is that the object is momentarily at rest relative to the observer. The velocity then continues decreasing to v=-10\text{ m/s} , implying that the object is now moving in the negative direction. A real-life scenario for this may be that you observe someone pulling into a long driveway, stopping briefly at the end, and then backing down it.

Velocity vs Time Graph for Multi-Stage Motion

Now, let’s return to our car from before that moved in the positive direction, stopped, and then came back. Since the slope in each segment of the position graph was constant, we assumed that the car’s movements had a constant velocity and that it had zero velocity when it stopped. The velocity-time graph for this motion would look a bit like this:

A velocity vs time graph can show multiple velocities for different time segments.

You can see that the velocity remains a constant v=1\text{ m/s} while the car moves to the right, changes to v=0\text{ m/s} while the car stops, and then becomes v=-1\text{ m/s} while the car moves back to the left. 

Finding Displacement from a Velocity vs Time Graph

Much like how we could find a velocity from a position-time graph, we can find displacement from a velocity-time graph. This process will be a bit different. Instead of finding the slope of the velocity graph, we will be finding the area under the velocity graph. This may sound counterintuitive, but we can prove that it works by checking our units. Let’s say that an object moves at 5\text{ m/s} for 10\text{ s} . The velocity-time graph for this motion would look like this:

A velocity vs time graph for an object with constant velocity is a horizontal line.

Proving Displacement is the Area under Velocity vs Time Graphs

To prove that the area under this velocity-time graph is the object’s displacement, let’s start with figuring out the displacement. The equation for displacement is \Delta x=vt . In this case, we know v=5\text{ m/s} and t=10\text{ s} . Therefore, \Delta x=(5\text{ m/s})\cdot (10\text{ s})=50\text{ m} .

Now that we know we’re looking for a displacement of 50\text{ m} , let’s try finding the area under the curve. Specifically, this is the area between the line of our graph and the x-axis. We’ll start by drawing a shape – in this case, a rectangle. We’ll also include values for its base and height.

The area under a velocity vs time graph is equal to the displacement.

It’s worth noting here that the units along each axis were also included for the base and height of the rectangle. The equation for the area under the curve is the one you would use to find the area of a rectangle, A=bh . So, let’s pull down our values and solve our equation:

  • b=10\text{ s}
  • h=5\text{ m/s}

As a result, we obtained the same numerical value of 50 , but more to the point we obtained the correct units. The area under the curve of a velocity graph will always be a displacement. Let’s look at a couple of more examples. If you’re uncertain about your ability to remember the equations for the area of a rectangle or triangle, it may be worth writing them in your notes or referencing a formula sheet such as this one .

Example 1: Finding Displacement for Multiple Velocities

The graph above was pretty simple, so let’s look at some more complex motion graphs. We can return to the velocity-time graph for our car that moved to the right, paused, then moved back to the left.

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We already know that our displacement for this motion is 0\text{ m} . Let’s start by sectioning off our graph here into shapes we cam find the area of. Again, we’re looking for the area between the line of the graph and the x-axis.

The area between the line and axis of a velocity vs time graph is the displacement.

It seems strange to have a negative value for the height of a shape as you’ve likely been told that area should always be a positive value. We’ll see why having a negative height when the graph is below the x-axis is both allowed and important. Now that we have all of our rectangles we can start finding their area.

Let’s begin with the rectangle farthest to the left.

  • b=5\text{ s}
  • h=1\text{ m/s}

Now we can solve for the area of our middle rectangle. This may seem like a trick question as it is, essentially, just a flat line, but we’ll still want to include it.

  • h=0\text{ m/s}

Finally, let’s find the area of the rectangle on the right. This has a negative value for its height so it should also have a negative area, strange as that may seem.

  • h=-1\text{ m/s}

Now that we know the area of all three rectangles, we’ll want to add those areas together to find the total area under the velocity-time curve and therefore also our total displacement.

Now, we see the expected value of 0\text{ m} that we’d found before. It’s important to note that this was only possible because one of our rectangles had a negative area.

Example 2: Finding Displacement with Changing Velocity

We know we can use rectangles to find the area under a velocity-time graph, but not all graphs are horizontal lines. Sometimes, graphs are diagonal which requires us to find the area of a different shape – a triangle. Consider the velocity-time graph.

A velocity vs time graph for an object that speeds up and then maintains its speed has a diagonal and a horizontal component.

We can create a rectangle on the right where the velocity is constant, but the area where it’s increasing will not look like a rectangle at all. Instead, this is where we’ll have to create a section that is a triangle.

The area under a velocity vs time graph can be composed of multiple shapes, including triangles and rectangles.

We now have two separate shapes. Much like when we had three separate rectangles, we’ll find the area of each shape individually and then add those two areas together to find the overall displacement for this motion. Let’s start with the triangle.

  • h=10\text{ m/s}

Now, we can find the area of the rectangle portion.

Finally, we’ll add these two values to find our total displacement:

Finding Acceleration from a Velocity vs Time Graph

At this point, it may not shock you to learn that the slope of a velocity-time graph can tell us just as much as the area under its curve. Instead of displacement, though, the slope of a velocity graph will tell us an object’s acceleration. Let’s consider the graph.

A velocity vs time graph for an object moving with a constant, positive velocity is a diagonal line.

The velocity of the object being shown in this graph is steadily increasing by 2\text{ m/s} every 1\text{ s} . With that information, we can prove that a=\Delta v/\Delta t=(2\text{ m/s})/(1\text{ s})=2\text{ m/s}^2 . Now that we know what our acceleration should be, let’s try to find it by finding the slope of the velocity time graph.

Proving Acceleration is the Slope of Velocity vs Time Graphs

If you remember from earlier, the slope of any given straight line can be found with the equation:

Let’s begin by selecting two points off of our graph above (being sure to include the units when we do). Let’s take (2\text{ s},4\text{ m/s}) and (4\text{ s},8\text{ m/s}) and plug the values in.

Again, this should look like a set of delta values – change in velocity over change in time, specifically. This is the definition of acceleration. While you may already be able to see how this will turn into proof that acceleration is the slope of a velocity graph, let’s keep going. What we’ll be looking for when we solve this equation this time will be a numerical value of 2 and units of m/s 2 .

Notice that we have a value that matches the acceleration we solved for before. We could have selected any two points on our graph and received the same result. The part of this that truly proves the slope of any velocity-time graph is the acceleration is that the units of our slope work out to be m/s 2 – the units for acceleration.

Example 1: Finding Negative Acceleration

Let’s consider the velocity vs time graph.

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We can see that the graph has a constant, negative slope so we can choose any two points we want and we should get the correct acceleration, which should also be a negative value. Whenever possible, it’s worth choosing values with zeros, so let’s select the points (0\text{ s},5\text{ m/s}) and (5\text{ s},0\text{ m/s}) . Now that we have our points, let’s pull out the values we need and plug them into our slope formula to solve for the acceleration of this object.

  • y_{2}=0\text{ m/s}
  • y_{1}=5\text{ m/s}

Example 2: Finding Multiple Accelerations

Let’s consider a more complex example with the velocity-time graph below.

A negative slope on a velocity vs time graph indicates a negative acceleration and a positive slope indicates a positive acceleration.

This graph has a change in its slope. This means we have two separate sections that we can look at: before t=5\text{ s} and after t=5\text{ s} .

Let’s consider the after t=5\text{ s} portion of the graph. Assuming that our acceleration will be negative because our velocity values are always negative is a common mistake among budding physicists. We’ll see here that this isn’t always true. Let’s choose the points (5\text{ s},-10\text{ m/s}) and (10\text{ s},-5\text{ m/s}) and plug these values into our slope formula.

  • y_{2}=-5\text{ m/s}
  • y_{1}=-10\text{ m/s}
  • x_{2}=10\text{ s}
  • x_{1}=5\text{ s}

If we plug these values into our slope formula, we can find that:

We see that even though our velocity values are negative, our slope is still positive so our acceleration must still be positive. Be careful when looking at motion graphs and making early assumptions. Things are sometimes more complicated than they appear.

Describing Motion with Acceleration vs Time Graph s

Last but not least, we can describe an object’s motion with an acceleration vs time graph. These will likely be graphs with zero slope while you are starting your study of motion graphs. You may find them becoming more complicated if you pursue a career in physics, but for now, we can keep things simple. The below graph is a standard example of an acceleration graph you may see.

Introductory motion graphs will typically only show acceleration vs time graphs with a constant or zero acceleration.

This graph actually shows acceleration due to gravity on Earth’s surface at a constant value of 9.81\text{ m/s}^2 . The other acceleration-time graph you’re likely to see in a high school physics class may look more like this:

Introductory motion graphs will typically only show acceleration vs time graphs with a constant or zero acceleration.

This would indicate that the object’s velocity is not changing, or perhaps that it isn’t moving at all. 

It is worth noting that the area under the curve of an acceleration vs time graph is equal to an object’s velocity, much like how the area under a velocity vs time graph is the displacement. Most high school physics classes won’t spend much time on this idea, but as you progress through your physics career this idea may come up. If you’d like to prove it to yourself, you could follow the same proof we used when proving the relationship between a velocity-time graph and an object’s displacement.

Pairing Motion Graphs

The last skill we’ll cover for motion graphs is determining which pair of graphs represent the same motion. We can make more than one graph to describe any given motion. For example, we had both a position-time graph and a velocity-time graph for our car moving to the right, pausing, and then coming back to the left. We can extend this idea to include acceleration graphs too. Let’s consider the three graphs you were presented with at the beginning of this article.

The key to interpreting motion graphs is being able to translate between different graphs.

We can see the position vs time graph on the left has a constant, positive slope. Since we know that velocity is the slope of a position vs time graph, our velocity must therefore be a constant, positive value. Indeed, we see that the velocity vs time graph here is constantly at 5\text{ m/s} . If we continue following this logic, we can assume that our acceleration should be zero as the slope of our velocity vs time graph is zero. And, again, we see that this holds true as the acceleration vs time graph is constant at 0\text{ m/s}^2 .

While it may be easy to see that these three motion graphs are connected after looking at them for a few moments, you’ll want to be able to compare more complex graphs throughout your physics career. There are a few steps you can take to achieve this goal.

The Steps to Pairing Motion Graphs

Step 1: observe the shape and make a prediction.

Odds are, you’ll see three different shapes when looking at position graphs, three shapes when looking at velocity graphs, and only two shapes when looking at acceleration graphs. Without even looking at the numbers on these graphs, the shapes can tell you a lot. Here are the shapes of each graph you may see throughout your high school physics career:

Common shapes for motion graphs, including position vs time graphs, velocity vs time graphs, and acceleration vs time graphs.

All of these examples are of positive values but know that they may be flipped. This would simply mean that the slope values are negative instead of positive. Just from glancing at the graphs above, even though they don’t have any number, you could match them up just by looking at the slopes.

Corresponding Shapes on Motion Graphs

Here’s a chart of how the different shapes match up.

Position-Time GraphsVelocity-Time GraphsAcceleration-Time Graphs
ParabolaDiagonalFlat
DiagonalFlatZero
FlatZeroZero

You may notice that the arrows here go both ways and for good reason. While you’ll need to do some math to know exactly which parabola-shaped position-time graph matches a diagonal-shaped velocity-time graph, those two shapes will always go together, regardless of which you start with.

Step 2: Decide if it is Positive or Negative

There is one more step you can take in matching up motion graphs before you start doing any actual math, which is looking for positive or negative slopes. Let’s look at this position-time graph.

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We can see that the slope here is negative. The curve is above the x-axis so the values are positive, but the slope itself is negative. We know that this shape of the position-time graph will go with a flat velocity-time graph, but we need to pick the right one. We may need some mathematics for this, but let’s first try to narrow down our options. Let’s say you had to pick between the three velocity-time graphs below.

Three different velocity vs time graphs.

We’ve decided that our graph should be a straight, horizontal line. All three of these graphs match that description. We also said that our slope is negative, and only two of the velocity-time graphs have negative values. So, without doing any mathematics, we know that the positive-time graph above will have to be paired with the middle velocity-time graph or the right velocity-time graph. To find out for sure, we’ll have to add some numbers and do some math.

Step 3: Calculate the Slope and Compare

Let’s take that same position-time graph and the two velocity-time graphs we couldn’t decide between. As you’ll see, they now have some numbers so that we can do some math to actually match the correct graphs.

A position vs time graph and two potential velocity vs time graphs.

We’ll need to begin by finding the slope of the position-time graph. To keep things simple, let’s use (0\text{ s},5\text{ m}) and (5\text{ s},0\text{ m}) . Now let’s pull out some values and solve for slope.

So, the velocity-time graph that matches our position-time graph here should have a value of -1\text{ m/s} . If we look, the velocity-time graph on the left has its line moving through -1\text{ m/s} so that must be the correct velocity-time graph.

We used these three steps of looking at the shape, looking at positive or negative, and then calculating the slope to go from a position-time graph to a velocity-time graph, but they can help us do much more than that. They can help us match up all three kinds of graphs or any pair of motion graphs – even a position-time graph and an acceleration-time graph.

Example 1: Which Pair of Graphs Represent the Same Motion?

Let’s consider the position-time graph below and try to match it to the correct velocity vs time graph.

Compare motion graphs to identify which ones represent the same motion.

Observe the Shape

Right off the bat, we know we have a parabola-shaped position-time graph. From that, we can narrow down our velocity-time graph options. A parabola position-time graph always goes to a diagonal velocity-time graph so we can cross off the middle graph immediately. Now we’re left with two different choices.

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You may think you have the right answer already (and indeed you might), but let’s think through this carefully. We already matched up our shapes so now it’s time to compare our positives and negatives.

Decide if it is Positive or Negative

The parabola in the position-time graph points upward so it has a positive slope. That means our velocity-time graph needs to be positive. If you’re thinking too carefully about slope, you may be drawn to the graph on the left. While it’s true that the graph on the left has a positive slope, it actually contains negative values. The values are what’s important here, not the slope. Instead, the graph on the right is the correct choice here. We knew we needed a diagonal velocity-time graph with positive values and we only had one option. You may often encounter examples like this, but be careful to always check your instincts before answering too quickly.

It is also worth noting here that a helpful trick for recognizing whether a velocity-time graph could give a positive slope to a position-time graph is if the curve of the velocity-time graph is over the x-axis. The same is true in reverse; a velocity-time graph with a curve below the x-axis will match with a position-time graph with a negative slope.

Example 2: Match the Velocity-Time Graph

The same principles that we just used above can also help us transition from a velocity-time graph to an acceleration-time graph. Let’s consider the set of motion graphs below.

Compare motion graphs to identify which ones represent the same motion.

From the start, we can see that we have a diagonal-shaped velocity-time graph so we can eliminate our middle acceleration-time graph. Although we will want a flat graph, the middle one is on the x-axis, which would imply that our velocity-time graph has zero slope. If that were the case, it would be flat instead of diagonal.

Now that we are again down to two graphs, let’s look at the positives and negatives. The velocity-time graph has a negative slope so we’ll want an acceleration-time graph with a curve below the x-axis. This leaves us with only one option – the graph on the right. 

Again, we didn’t need to get to the mathematics. You could check the values if you wanted to, but often looking just at the shapes of your graphs will be enough. Just make sure you always think through both the shape of your motion graphs and if your positives and negatives line up.

Physicists use motion graphs to visualize data all the time. While the different types and shapes may be confusing at first, getting comfortable with them will help you make connections between the kinematics terms you’ve learned so far. It can also help you simplify problems by being able to visualize what the problem is asking you in a different way. If you take the time to get comfortable reading each time of motion graph, deriving different values from them, and matching them up, you’ll be well on your way to visualizing data the way research scientists do every day.

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