A car starts from rest and moves with uniform acceleration a on a straight road from time `t=0` to `t=T`. After that, a constant deceleration brings it to rest. In this process the average speed of the car is

Options

A. `(aT)/(4)`
B. `(3aT)/(2)`
C. `(aT)/(2)`
D. `aT`

Answer

C

Explanation

When accelerate
`(S_1) = 1/2 v_m T = 1/2 aT^2`
When retardation
Stoping distance`S_2 = (v_m^2)/(2a_1)`
` = (v_m^2)/(2. (v_m)/(T_1)) = (aT xx T_1)/(2)`

`v_(avg) = (1/2 aT^2 + 1/2 a xx T xx T_1)/(T + T_1)`
`= 1/2 aT` .