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A car accelerates from rest at a constant rate $α$ for some time, after which it decelerates at 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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$(\frac{α^{2} + β^{2}}{α β}) t$

$(\frac{α^{2} - β^{2}}{α β}) t$

$\frac{(α + β) t}{α β}$

$\frac{α β t}{α + β}$

answer is C.

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Detailed Solution

$α = \frac{v}{t_{1}} \Rightarrow t_{1} = \frac{v}{α}, β = \frac{v}{t_{2}} \Rightarrow t_{2} = \frac{v}{β}$

$t = t_{1} + t_{2} = \frac{v}{α} + \frac{v}{β}$

$v = \frac{α β t}{α + β}$

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