Rest and Motion

An object is said to be at rest if its position does not change with respect to its surroundings with the passage of time.
An object is said to be in motion if its position changes with respect to its surroundings with the passage of time.
Both rest and motion are not absolute. They depend on the observer and the surroundings chosen for observation.

Relativity of Rest and Motion

Rest and motion are relative terms. The same object can be at rest for one observer and in motion for another observer at the same time.
For example, a passenger sitting inside a moving bus is at rest with respect to the bus. The same passenger is in motion with respect to a person standing on the roadside.
This shows that rest and motion depend on the observer’s point of view.

There is no object in the universe that can be said to be in absolute rest or absolute motion.

Frame of Reference

To describe rest or motion clearly, we must choose a reference point or a set of reference points. This is called a frame of reference.
A frame of reference is a set of coordinates or surroundings relative to which the position of an object is measured.
Without a frame of reference, it is impossible to decide whether an object is at rest or in motion.

Need for Frame of Reference

Motion cannot be described in isolation. It is always described relative to something else.
For example, when we say a car is moving, we actually mean that the car is moving relative to the road or the ground.
If the frame of reference changes, the description of motion also changes.

Types of Frame of Reference

Rest Frame

A frame of reference in which the observer is at rest.
Example: A person standing on the ground observing a moving train.

Moving Frame

A frame of reference that itself is moving.
Example: A passenger sitting inside a moving train observing another passenger.

Position of an Object

The position of an object is its location with respect to a chosen reference point.
Position is usually described using distance and direction.
For one-dimensional motion, position can be described using a straight line and a reference point called the origin.

Distance

Distance is the total length of the actual path travelled by an object between two points.
Distance is a scalar quantity. It has magnitude only and no direction.
Distance is always positive or zero.
Distance depends on the actual path followed by the object.

Displacement

Displacement is the shortest straight-line distance between the initial and final positions of an object, along with direction.
Displacement is a vector quantity. It has both magnitude and direction.
Displacement can be positive, negative, or zero.
Displacement depends only on initial and final positions, not on the path followed.

Difference Between Distance and Displacement

Distance represents how much ground an object has covered.
Displacement represents how far an object is from its starting point in a particular direction.
If an object returns to its starting point, distance is non-zero but displacement is zero.

Motion

Motion is defined as the change in position of an object with respect to time and a chosen frame of reference.
If the position of an object changes continuously with time, the object is said to be in motion.

Time in Motion

Time is an essential factor in describing motion.
Without considering time, we cannot decide whether an object is moving fast or slow.
Motion always involves change in position with time.

Types of Motion

Motion can be classified based on the nature of movement.

Translational Motion

In translational motion, the object moves from one place to another.
Every point of the object moves the same distance in the same direction.
Examples include a car moving on a straight road and a train moving on a track.

Rectilinear Motion

Rectilinear motion is a type of translational motion in which an object moves along a straight line.
Examples include a stone falling vertically and a car moving on a straight highway.

Curvilinear Motion

Curvilinear motion is a type of translational motion in which an object moves along a curved path.
Examples include a car taking a turn on a curved road and a thrown ball moving in a curved path.

Circular Motion

Circular motion is a special type of curvilinear motion in which an object moves along a circular path.
Although the speed may remain constant, the direction of motion keeps changing.
Examples include the motion of the hands of a clock and a stone tied to a string and rotated in a circle.

Rotational Motion

In rotational motion, an object rotates about a fixed axis.
Different parts of the object move in circles around the axis.
Examples include a spinning wheel and the rotation of the Earth about its axis.

Oscillatory Motion

In oscillatory motion, an object moves back and forth about a fixed mean position.
The motion is repeated at regular intervals.
Examples include the motion of a pendulum and the vibration of a spring.

Periodic Motion

Periodic motion is a motion that repeats itself after equal intervals of time.
Oscillatory motion is always periodic, but not all periodic motions are oscillatory.
Example: The revolution of the Earth around the Sun is periodic but not oscillatory.

Uniform Motion

An object is said to be in uniform motion if it covers equal distances in equal intervals of time.
The speed of the object remains constant.
Uniform motion can occur in a straight line or along a curved path, but direction must remain constant for velocity to be uniform.

Non-Uniform Motion

An object is said to be in non-uniform motion if it covers unequal distances in equal intervals of time.
The speed or direction or both change with time.
Most natural motions are non-uniform.

Speed

Speed is defined as the distance travelled by an object per unit time.
Speed is a scalar quantity.
It tells how fast an object is moving but does not tell the direction of motion.

Average Speed

Average speed is defined as the total distance travelled divided by the total time taken.
Average speed depends on the total path length.

Instantaneous Speed

Instantaneous speed is the speed of an object at a particular instant of time.
Speedometers in vehicles show instantaneous speed.

Velocity

Velocity is defined as displacement per unit time.
Velocity is a vector quantity. It has both magnitude and direction.
Velocity gives information about both speed and direction of motion.

Average Velocity

Average velocity is defined as total displacement divided by total time taken.
If displacement is zero, average velocity is zero even if distance covered is not zero.

Uniform Velocity

An object is said to have uniform velocity if it covers equal displacements in equal intervals of time in the same direction.
Both magnitude and direction of velocity remain constant.

Acceleration

Acceleration is defined as the rate of change of velocity with respect to time.
Acceleration occurs if there is a change in speed, direction, or both.
Acceleration is a vector quantity.

Types of Acceleration

Positive Acceleration

Acceleration is positive when velocity increases with time.

Negative Acceleration or Retardation

Acceleration is negative when velocity decreases with time.
This is also called retardation.

Uniform Acceleration

Uniform acceleration occurs when velocity changes by equal amounts in equal intervals of time.
Example: A freely falling body near the surface of the Earth.

Non-Uniform Acceleration

Non-uniform acceleration occurs when velocity changes by unequal amounts in equal intervals of time.

Motion in One, Two, and Three Dimensions

One-Dimensional Motion

Motion along a straight line.
Example: Motion of a car on a straight road.

Two-Dimensional Motion

Motion in a plane.
Example: Projectile motion.

Three-Dimensional Motion

Motion in space.
Example: Motion of a bird flying freely in the air.

Rest and Motion Are Relative, Not Absolute

There is no fixed point in the universe that can be taken as an absolute reference.
Even the Earth is moving around the Sun, and the Sun itself is moving in the galaxy.
Therefore, rest and motion depend entirely on the chosen frame of reference.

Common Misconceptions Related to Rest and Motion

Rest does not mean absence of motion in all senses. An object at rest on Earth is still moving with the Earth.
Motion does not always require speed to change. An object moving in a circle at constant speed is still in motion because its direction changes.
Zero displacement does not mean zero distance.

What Rest and Motion Do Not Include

Rest and motion do not describe the cause of movement.
They only describe the state of movement or non-movement.
Force is required to change the state of rest or motion, but force is not part of the definition of motion.

Boundary Conditions

Classical definitions of rest and motion apply at everyday speeds.
At speeds close to the speed of light, classical mechanics becomes inadequate, and relativistic mechanics is used.
However, for NDA, CDS, AFCAT, and CAPF level questions, classical definitions are sufficient.

Importance of Rest and Motion in Mechanics

All laws of motion are based on the understanding of rest and motion.
Concepts like force, momentum, and energy depend on motion.
Kinematics, which deals with motion without considering forces, begins with rest and motion.

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