# Motion In A Straight Line Class 11 Notes Physics Chapter 3 - CBSE

## What Are Motion In A Straight Line ?

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## Motion

An object is said to be in motion if its position changes with time.

## Branches In Physics

Kinematics

• It describes the motion of objects, without looking at the cause of the motion.

Dynamics

•  It relates the motion of objects to the forces which cause them.

## Difference Between Distance & Displacement

Distance

For a particle in motion the total length of the actual path traversed between initial and final positions of the particle is known as the ‘total path length’ or distance covered by it. The S.I unit of distance is meter. It is a scalar quantity.

Displacement

Displacement of a particle in a given time is defined as the change in the position of particle in a particular direction during that time. It is given by a vector drawn from its initial position to its final position. The S.I unit of displacement is meter. It is a vector quantity.

## Difference Between Speed & Velocity

Speed

It is the rate at which a particular distance is covered by an object. Its S.I unit is m/s. It is a scalar quantity.

Velocity

Velocity refers to the rate at which an object changes their position in a particular direction. Its S.I unit is m/s. It is a vector quantity.

## Types of Motion

Uniform Motion

• An object is said to be in uniform motion in a straight line if its displacement is equal in equal intervals of time.

Non-Uniform Motion

• An object is said to be in non-uniform motion if its displacement is unequal in equal intervals of time or vice-versa.

## Difference Between Average Speed & Velocity

Average Speed

• It is the ratio of total path length traversed and the corresponding time interval.

Average Velocity

• Average velocity is calculated by dividing displacement (a vector pointing from initial position to final position) by the total time.
• $$\Delta v =\frac{\Delta x}{\Delta t}$$

The average speed of an object is greater than or equal to the magnitude of the average velocity over a given time interval.

## Difference Between Instantaneous Speed & Velocity

Instantaneous Speed

• Instantaneous speed is the limit of the average speed as the time interval becomes infinitesimally small.

Instantaneous Velocity

• Instantaneous velocity or simply velocity is defined as the limit of the average velocity as the time interval ∆t becomes infinitesimally small.

## Acceleration

The rate of change of velocity is called acceleration. Its S.I unit is ms-2.

$$a =\frac{(v-u)}{t}$$

a=acceleration, v=final velocity, u=initial velocity, t=time

## Types of Acceleration

Uniform Acceleration

• If an object undergoes equal changes in velocity in equal time intervals, it is called uniform acceleration.

Non-uniform Acceleration

• An object is said to be with non uniform acceleration if the velocity of the object changes by unequal amounts in equal intervals of time.

## Position Time Graph

The graph on which the instantaneous position x of a particle is plotted on the y-axis and the time t on the x-axis is known as the Position-Time graph.

## Velocity Time Graph

A graph drawn by taking time along the x-axis and velocity along the y-axis is called a velocity-time graph.

## Newton’s Law Of Motion

For uniformly accelerated motion, some simple equations can be derived that relate displacement (x), time taken (t), initial velocity (u), final velocity (v) and acceleration (a). Following equations give a relation between final and initial velocities v and u of an object moving with uniform acceleration

v = u + at

$$s =\text{ut +}\frac{1}{2}\text{at}^{2}$$

v2 = u2 + 2as

## Relative Velocity

Relative velocity is defined as the velocity of an object B in the rest frame of another object A. The velocity of the object A relative to the object B can be given as,

Vab = Va - Vb