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 of magnitude $a$ brings it to rest. In this process the average speed of the car is

• A. $\frac{aT}{4}$
• B. $\frac{3aT}{2}$
• C. $\frac{aT}{2}$
• D. $aT$

Answer 1

Answer: (C)

Distance while accelerating
$X_1=\frac{1}{2}a{T}^2$ ......(1)
Velocity $v=aT$ .......(2)
Time taken during deceleration
$0=\left(aT\right)-at$
$t=T$
$\therefore$ Distance while decelerating
$x_2=\left(aT\right)T-\frac{1}{2}a{T}^2$
$x_2=\frac{1}{2}a{T}^2$ .......(3)
Average Speed $=\frac{x_1+x_2}{T+T}$
$v_{av}=\frac{\frac{1}{2}a{T}^2+\frac{1}{2}a{T}^2}{2T}$
$v_{av}=\frac{aT}{2}$