Question

If the velocity of a body changes from 13 m/s to 30 m/s while undergoing constant acceleration, what's the average velocity of the body?

A. 28 m/s
B. 17 m/s
C. 21.5 m/s
D. 19.5 m/s

Answer 1

The answer is 21.5 m/s

Answer 2

Since the acceleration is constant, the average velocity is simply the average of the initial and final velocities of the body:

`v_(avg) = (v_f+v_i)/(2)=(30 m/s+13 m/s)/(2)=21.5 m/s`

We can proof that the distance covered by the body moving at constant average velocity
`v_(avg)` is equal to the distance covered by the body moving at constant acceleration a:

- body moving at constant velocity
`v_(avg)`: distance is given by

`S=v_(avg)t = (v_f+v_i)/(2)t`

- body moving at constant acceleration
`a=(v_f-v_i)/(t)`: distance is given by

`S=v_i t+ (1)/(2)at^2 = v_i t + (1)/(2)(v_f-v_i)/(t)t^2=(v_i+(1)/(2)(v_f-v_i))t=(v_f+v_i)/(2)t`