# Formula For Acceleration

## Formula for Acceleration

It is defined as rate of change of velocity with respect to time.

It is a vector quantity. Its S.I. unit is m/s2 and dimension is [LT-2]

### (a) Instantaneous acceleration

Instantaneous acceleration is the limiting value of average acceleration as △t approaches to zero

Instantaneous acceleration is equal the derivative of the velocity with respect to time.

Slope of the tangent on v-t graph gives the instantaneous acceleration.

Instantaneous acceleration also known as acceleration

instantaneous acceleration

When the acceleration is constant, the time interval in which change takes place.

Suppose a particle moving along x-axis has velocity v1 at time t1 and velocity v2 at time t2 average acceleration.

### (b)Average acceleration

It is defined as ratio of change in velocity to the time interval in which change takes place. Suppose a particle moving along x-axis has velocity v1 at time t1 and velocity v2 at time t2 average acceleration aav is given by

### Examples of Acceleration

Q1: A bus accelerates with an initial velocity of 10 m/s for 5s then 20 m/s for 4s finally for 15 m/s for 8s. What can be said about the average acceleration of the bus?

Ans: It is given that, the velocities of the bus at different time intervals is, v1 = 10 m/s, v2 = 20 m/s, v3 = 15 m/s

The time intervals for which the object possesses these velocities are t1 = 5s, t2 = 4s, t3 = 8s

Hence, over the interval, the total velocity can be given as the sum of these velocities.

Similarly, the total time interval can be given as the sum of these intervals.

△t = t1 + t2 + t3 = 5 + 4+ 8 = 17s

Using the above formula for average acceleration, we get.

Average Acceleration = △u /△t

Average Acceleration = 45./17 = 2.65 m/s2

Q2: A sparrow, while going back to its nest accelerates to 6 m/s from 3 m/s in 5s. What can we say about its average acceleration?

Ans: Given : The initial velocity, vi = 3m/s

The final velocity, vf = 6m/s

Total time for which the acceleration takes place, t = 5 s