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

For first part,
`u = 0, t = T` and acceleration `= a`
`:. v = 0 + aT= aT` and `S_1 = 0 + (1)/(2) aT^2 = (1)/(2) aT^2`
For second part,
`u = aT`, retardation `= a_1, v = 0` and time taken`= T_1` (let)
`:. 0 = u - a_1 T_1 rArr aT = a_1 T_1`
and from `v^2 = u^2 - 2 aS_2 rArr S_2 = (u^2)/(2 a_1) = (1)/(2) (a^2 T^2)/(a_1)`
`S_1 = (1)/(2) aT xx T_1" "("As " a_1 = (a T)/(T_1))`
`:. v_(av) = (S_1 + S_2)/(T + T_1) = ((1)/(2) aT^2 + (1)/(2) aT xx T_1)/(T + T_1)`
=`((1)/(2) aT(T + T_1))/(T + T_1) =(1)/(2) aT`.