Question

A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t sec, evaluate the maximum velocity reached.

Answer 1

Thus, its velocity-time graph is a staright line OA sloping in the upward direction.the maximum velocity of the car be considered to be 'v'.

The slope of the graph OA gives the accelration of the car.

$\alpha =\frac{v}{t_1}.......\left(1\right)$

The car begins decelerate after attaining the maximum velocity.Thus, its velocity-time graph is a straight line AB sloping in the downward direction.The slope of the graph AB gives the detardation of the car.

$\beta =\frac{v}{t-t_1}........\left(2\right)$

$t=v(\frac{1}{\alpha }+\frac{1}{\beta })$

$v=\left(\frac{\alpha \beta }{\alpha +\beta }\right)t$