A car accelerates from rest at a constant rate $α$ for some time, after which it decelerates at a constant rate $β$ and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

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$\frac{(α + β) t}{α β}$

$(\frac{α^{2} - β^{2}}{α β}) t$

$(\frac{α^{2} + β^{2}}{α β}) t$

$\frac{α β t}{α + β}$

answer is C.

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Detailed Solution

Let maximum velocity $= V$

Now $V = 0 + α t,$

Similarly $0 = V - β t$

From the above equations we get

$t_{1} = \frac{V}{α}$ and $t_{2} = \frac{V}{β}$

$\begin{aligned} t = t_{1} + t_{2} \\ t = \frac{V}{α} + \frac{V}{β} \\ t = V [\frac{α + β}{α β}] \\ ∴ V = \frac{α β t}{α + β} \end{aligned}$

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