The general study of the relationship between motion, force and energy is known as mechanics. It is subdivided into three branches, i.e., kinematics, dynamics and statics. Kinematics deals with the study of the motion of objects without taking into account the forces and energies that may be involved. The first thing we need to understand is that there is no absolute rest or absolute motion. Rest and motion are relative terms.
Download Complete Chapter Notes of Motion in One Dimension
Download Now
In simple terms, an object that changes its position is said to be in motion, while the opposite action causes an object to be at rest. However, perspective plays a huge role in it. Take the example of an atom which is always in motion, but when we see an object in the macro world, it seems to be at rest. Therefore, both rest and motion depend mainly on the frame of reference of the one who is observing the scene.
Table of Contents
 Rest and Motion Definition
 Rest and Motion Related Terms
 Equations of Uniformly Accelerated Motion
 Displacement, Velocity and Time Graphs
 Types of Motion
 Important Points
Rest and Motion Definitions
Rest: An object is said to be at rest if it does not change its position with respect to its surroundings with time.
Motion: An object is said to be in motion if its position changes with respect to its surroundings and time.
Frame of Reference
Suppose an object is placed on a table; it can be said that the object is at rest. If a person is standing on the moon, he will observe that the earth is changing its position continuously, and so are the table and the object. Thus, to locate the position of anything, one needs to define a frame of reference. For instance, if we take the earth as a reference, then the object is at rest, but if the moon is taken as a reference, the object is in motion. A frame of reference can be inertial or noninertial, depending on whether it is at rest or constantly moving.
Rest and Motion Related Terms
Speed
The distance covered by a moving body in a unit time interval is called its speed. It can be either uniform or nonuniform. Its units are metres per second (m/s)
Speed = [Distance Travelled]/[Time Taken]
Speed is generally shown in a positiontime graph.
 Uniform motion: When a body covers an equal distance in an equal interval of time.
 NonUniform Motion: The body covers an unequal distance in an equal interval of time.
Displacement
It is defined as the shortest distance between the initial position and the final position.
Velocity
Change in the displacement of the body with respect to time is called its velocity. It is a vector quantity, i.e., it has both magnitude and direction.
Velocity = Displacement/Time
 Uniform velocity: Magnitude and direction remain the same with respect to time.
 Nonuniform velocity: When the body covers unequal displacement in an equal interval of time in a particular direction or if the direction changes, it is said to be moving at nonuniform velocity.
 Average velocity = Time displacement/Total time taken.
Acceleration and Deceleration
A body is said to be in acceleration if it gradually increases its velocity with respect to time.
Average acceleration = [Change in Velocity]/[Time taken] = Δy/Δt
Instantaneous acceleration =
Centripetal Acceleration
When a body moves along a circular path of radius R with constant speed (v), the velocity of the body keeps changing since the direction of the motion keeps changing. This change in velocity causes the body to experience an acceleration which is directed towards the centre of the circular path. This acceleration is called centripetal acceleration.
Equations of Uniformly Accelerated Motion
If a body starts its motion, along a straight line, with initial velocity ‘u’ and attains final velocity ‘v’ in the time interval ‘t’, the assumption used in all the equations is that the body covers distance ‘s’ at constant acceleration.
These equations are as follows:
 V = u + at
 S = ut + (1/2) at^{2 }
 V^{2 = }u^{2} + 2as
Important points:
 Acceleration and deceleration are vector quantities with SI unit m/s^{2}.
 A body is said to be decelerating if its velocity decreases with time.
 If acceleration does not change with time, it is said to be constant acceleration.
 Replace ‘a’ with acceleration due to gravity ‘g’ for a freely falling body. Similarly, if the body is thrown vertically upwards, replace ‘a’ with ‘g’.
 The slope of the displacementtime graph gives velocity, and the slope of the velocitytime graph gives acceleration.
Displacement, Velocity and Time Graphs
Different cases of the displacementtime graph (in the angle of the slope).
Sl. No.  Different Cases  st Graph  Main Features 
1  At rest  Slope ‘v’ = 0  
2  Uniform motion  θ = constant v = constant a = 0 

3  Uniform accelerated motion with u = 0, s = 0 at t = 0  θ is increasing. So ‘v’ is increasing and ‘a’ is positive  
4  Uniform accelerated motion with u ≠ 0, but s = 0 at t = 0  The slope of the st graph gradually goes on increasing  
5  Uniformly retarded motion  θ is decreasing. So, ‘v’ is decreasing and ‘a’ is negative 
Different cases of the velocitytime graph.
Sl. No.  Different Cases  vt Graph  Main Features 
1  Uniform motion  θ = 0 degrees v = constant slope a = 0 

2  Uniform accelerated motion with u = 0, s = 0 at t = 0  θ = constant a = constant v is increasing uniformly with time 

3  Uniform accelerated motion with u ≠ 0, but s = 0 at t = 0  Positive constant acceleration because θ is constant, but the initial velocity of the particle is positive  
4  Uniform accelerated motion  Slope of vt graph = a (retardation)  
5  Nonuniformly accelerated motion  The slope increases with time, that is, ‘a’ increases  
6  Nonuniformly accelerating motion  θ is decreasing. So, acceleration is decreasing 
Types of Motion
Projectile Motion
The motion of a body when it is thrown or projected with some initial velocity in a plane is known as projectile motion.
Examples:
 The motion of a golf ball.
 The motion of a rocket after burnout
 The motion of a bomb dropped from an aeroplane, etc.
Projectile motion is of two types:
 Horizontal projection
 Angular projection
Horizontal Projection
When a body is projected along the horizontal direction with an initial velocity of ‘u’, the projection is known as horizontal projection. It is assumed that there is negligible air resistance.
Velocity at any time t,
The direction of velocity, θ = tan ^{1} (gt / u)
Time of flight,
Range,
Angular Projection
When a body is thrown or projected at an angle with the horizontal direction, it is known as angular projection. It is assumed that air resistance is zero. The following equation of motion can be derived by examining the motion in the horizontal and vertical directions.
Equation of trajectory,
Y = x tan – ½ g [ x / u cos θ ] ^{2}
Time of flight, T = (2u sin θ)/g
Maximum height, H = [u^{2} sin^{2} θ]/[2g]
Range, R = [u^{2} sin2θ]/g
Circular Motion
The motion of an object along a circular path is called circular motion.
Important Points to Remember
 When a body moves along a circular path at a constant speed, the motion of the body is known as uniform circular motion.
 The direction of velocity at any point in a circular motion is given by the tangent to the circle at that point.
 In a uniform circular motion, both the velocity and acceleration change due to continuous changes in direction.
 When the speed of the body keeps changing while moving along the circular path, the motion is called a nonuniform circular motion.
 The magnitude of centripetal acceleration, a_{c} = y^{2} / R
Frequently Asked Questions on Rest and Motion
Are rest and motion relative terms?
While sitting inside a moving car, you will notice that you appear to be moving while gazing outside. And while looking up at the car’s roof, you will feel that you are at rest. Therefore, rest and motion are relative words.
What is meant by translatory motion?
When an object, such as a car, moves in a straight line and each of its points travels the same distance in the same amount of time, it is said to be in translatory motion.
Explain rotatory motion with an example.
Rotatory motion occurs when a body moves around a fixed axis without changing the radius of its motion. A spinning wheel is an example.
Comments