## Introduction

**Rest:** A body is said to be in a state of rest when its position does not change with respect to

a reference point.

#### Motion:

A body is said to be in a state of motion when its position change continuously with

reference to a point.

#### What is a reference point?

Generally, the position of an object needs to be defined with respect to a fixed point in

space. This point is often referred to as the origin.

#### Frame of Reference

**Depending on the frame of reference, an object may appear stationary or moving to a person. **

For example,

- For a person in a moving bus, the tree outside will appear to be moving in the opposite direction as the motion of bus.

- A person observing another person in a moving bus will appear to be in rest with respect to his/her position.

#### Types of Motion depending upon the Path:

**(i) Circulatory motion/Circular motion** â€“ When an object moves in a circular path.

**(ii) Linear motion** â€“ When an object moves in a straight line path.

**(iii) Oscillatory/Vibratory motion** â€“ When an object moves to and fro path with respect to a fixed point.

#### What are Scalar and Vector Quantities?

**Scalar quantity:** It is the physical quantity having own magnitude but no direction e.g., distance, speed.

**Vector quantity:** It is the physical quantity that requires both magnitude and direction e.g., displacement, velocity.

#### Distance and Speed

**Distance:** The actual path or length travelled by a object during its journey from its initial position to its final position is called the distance.

Unit of distance is meters (m).

It is a scalar quantity. It can only be positive.

Distance can be equal to displacement in a linear path.

**Displacement:** It is the shortest length between initial position and final position of an object.

It is a vector quantity.

It can be positive or negative depending upon the direction.

Displacement can be equal or lesser than the distance.

**Speed: **Rate of change of distance is called as speed. Therefore, speed is also a scalar quantity.

Speed can also be thus only positive.

**Velocity:** Rate of change of displacement is called as velocity. Therefore, velocity is a vector quantity.

Velocity can be negative or positive

**Acceleration:** Rate of change of velocity is called as acceleration.

An object in which the velocity is constant is said to have zero acceleration.

An object with uniform change in velocity is said to be uniformly accelerated or uniformly de-accelerated.

#### What is De-acceleration/Retardation?

When the velocity of an object decreases with time, the body is said to be de-accelerating or it is said to be in retardation.

**Uniform Motion:** When a body travels equal distance in equal interval of time, then the motion is said to be uniform motion.

A uniform motion has constant speed. It may or may not have constant velocity.

#### Why not constant velocity?

When an object is moving in a circular path at constant speed, its speed is constant but since its direction is changing, its velocity is also changing and hence it has an acceleration.

**Graphs for Uniform Motion in a Straight Line**

**Non-uniform Motion:** In this type of motion, the body will travel unequal distances in equal intervals of time.

**Distance â€“Time Graphs for Non-Uniform Motion in Straight Line**

**Velocity Time Graph for Non-Uniform Motion In Straight Line**

**Acceleration Time Graph for Non-Uniform Motion In Straight Line**

#### Understanding Graphs

**Points to Remember: **

**1. A flat graph represents no change in one variable.**

** Zero Velocity = Same Position**

**2. Zero Acceleration = Same Velocity**

**3. A steeper graph represents faster change Orange Graph represents greater acceleration than Green Graph**

**Equations of Motion with Graphical Derivation (For Uniformly Accelerated Motion)**

#### Uniform Circular Motion:

If a body is moving in a circular path with uniform speed, then it is said to be executing uniform circular motion.

In such a motion the speed may be same throughout the motion but its velocity (which is tangential) is different at each and every point of its motion.

Thus, uniform circular motion is an accelerated motion.

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