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
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