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A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is
Explanation
In fig., $AA_{1} = v_{max} = \alpha t_{1} = \beta t_{2}$ But $t = t_{1} + t_{2} = v_{max}/\alpha + v_{max}/\beta$ = $v_{max}(1/\alpha + 1/\beta) = v_{max}((\alpha + \beta)/\alpha\beta)$ or, $v_{max} = t(\alpha\beta/(\alpha + \beta))$