Rate of change of velocity

Acceleration:- Acceleration of a body is defined as the rate of change of its velocity with time. That is called acceleration.

acceleration = Change in velocity/ Time taken for change

Now, the change in velocity is the difference between the final velocity and the initial velocity. That is,

acceleration = Final velocity – Initial velocity/ Time taken

a = 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 the change in velocity

If the velocity of an object changes from an initial value u to the final value v in time t, this kind of motion is known as accelerated motion. The acceleration is taken to be positive if it is in the direction of velocity and negative when it is opposite to the direction of velocity. The S.I unit of acceleration is m s^-2.

Uniform Acceleration:- A body has a uniform accelerated if it travels in a straight line and its velocity increases by equal amounts in equal intervals of time. Ex- The motion of a freely falling body is an example of uniformaly accelerated motion.

Non-uniform Acceleration:- A body has a non-uniform if its velocity increases by unequal amounts in equal intervals of time. Ex- If a car travelling along a straight road increases its speed by unequal amounts in equal intervals of time, then the car is said to be moving with non- uniform acceleration.

Ex- Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of 6 m s^-1 in 30 s. Then he applies brakes such that the velocity of the bicycle comes down to 4 m s^-1 in next 5 s. Calculate the acceleration of the bicycle in both the cases.

Sol:- In the first case:

initial velocity (u) = 0

final velocity ( v) = 6 m s^-1

time (T) = 30 s

a = v – u/ t

a = (6m s^-1 – 0 m s^-1)/30 s

= 0.2 m s^-2

In second case:

initial velocity (u) = 6 m s^-1

final velocity (v) = 4 m s^-1

time (t) = 5 s

a = ( 4 m s^-1 – 6 m s^-1)/ 5 s

= – 0.4 m s^-2

The acceleration of the bicycle in the first case is 0.2 m s^-2 and in the second case, it is – 0.4 m s^-2