# Physics 9th: Motion | Acceleration and Retardation

## Physics 9th: Motion | Acceleration and Retardation

### ACCELERATION

We notice that bodies do change their speed or velocity. For example if we see the speedometer of a car, we will notice that the needle keeps on moving, that is the velocity of the car keeps on changing. The rate at which this change in velocity occurs, is known as acceleration.

\     Acceleration of a body can be defined as the rate of change of velocity with time

$\displaystyle Acceleration=\frac{Change\,\,in\,\,velocity}{Time\,\,taken\,\,for\,\,change}$

$\displaystyle Acceleration=\frac{Final\,\,velocity-Initial\,\,velocity}{Time\,\,taken}$

$\displaystyle a=\frac{v-u}{t}$

Where         a = Acceleration of the body

v = Final velocity of the body

u = Initial velocity of the body

t = Time taken for this change in velocity

·    S.I. unit of acceleration is $\displaystyle m{{s}^{-2}}$ (meter per Second Square)

·    Acceleration is a vector quantity

·    When a body is moving with uniform velocity, its acceleration is zero (or no acceleration)

This is because there is no change in velocity as initial velocity = Final velocity.

·    A body moving with non-uniform velocity is said to be in accelerated motion.

### Question:     Calculate the acceleration of a body which covers a distance of 50 m in every second while moving on a straight road.

Solution:

Velocity (A to B)$\displaystyle =\frac{50}{1}$

(u) = 50 m/s

Velocity (B to C)$\displaystyle =\frac{50}{1}$

(v) = 50 m/s

$\displaystyle a=\frac{v-u}{t}=\frac{50-50}{2}=0$

Therefore, in case of uniform motion, acceleration is zero

### Question:     Calculate the acceleration of a body which covers a distance of 50 m in one second and 70 m in next one second while moving on a straight road.

Solution:

$\displaystyle velocity=\frac{50}{1}$

(u) = 50 m/s

$\displaystyle velocity=\frac{70}{1}$

(v) = 70 m/s

$\displaystyle a=\frac{v-u}{t}=\frac{70-50}{2}=\frac{20}{2}=10$ m/s2

#### Uniform acceleration

A body has uniform acceleration when it travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time.

It can also be said that when the velocity of a body changes at a uniform rate, it is said to have uniform acceleration.

#### Non-uniform acceleration

A body is said to have non-uniform acceleration if its velocity increases or decreases by unequal amount in equal intervals of time

OR

When the velocity of a body changes at unequal rate or non-uniform rate.

#### Negative acceleration (retardation or deceleration)

Till now we have seen the case of increasing velocities. In many cases, there is also a decrease in velocity. For example when we apply brakes, the car stops after some time.

Therefore, if the velocity of the body increases, Acceleration is said to be Positive Acceleration

And if the velocity of a body decreases, acceleration is said to be Negative Acceleration, which is also called as Retardation or Deceleration.

Retardation is measured in the same way as acceleration.

$\displaystyle Retardation=\frac{v-u}{t}$

·    S.I. unit of retardation is $\displaystyle m{{s}^{-2}}$

·    Value of retardation is always negative as in this case ‘u’ is always larger than ‘v’