Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

For first part,

u=o,t=T and acceleration =a

$\therefore$ v=0+aT and $S_1=0+\frac{1}{2}a{T}^2=\frac{1}{2}a{T}^2$

For Second part,

u=aT, Retardation, $a_1=0,v=0$ and time taken$=T_1\left(let\right)$

$\therefore 0=u-a_1{T}_1\Rightarrow aT=a_1{T}_1$

and from $v^2=u^2-2a{S}_2\Rightarrow S_2=\frac{u^2}{2a_1}=\frac{1}{2}\frac{a^2{T}^2}{a_1}$

$S_2=\frac{1}{2}aT\times T_1$ $(As{a}_1=\frac{aT}{T_1})$

$\therefore V_{av}=\frac{S_1+S_2}{T+T_1}=\frac{\frac{1}{2}a{T}^2+\frac{1}{2}aT\times T_1}{T+T_1}$

$=\frac{\frac{1}{2}aT(T+T_1)}{T+T_1}=\frac{1}{2}aT$