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  4. 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

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Q. 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

NTA AbhyasNTA Abhyas 2020Motion in a Straight Line

Solution:

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