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Two cars P and Q start from a point at the same time in a straight line and their positions are represented by $x_{p} (t) = a t + b t^{2}$ and $x_{Q} (t) = f t - t^{2}$ .At what time do the cars have the same velocity?

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$\frac{a + f}{2 (1 + b)}$

$\frac{f - a}{2 (1 + b)}$

$\frac{a - f}{1 + b}$

$\frac{a + f}{2 (b - 1)}$

answer is B.

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Detailed Solution

$V_{P} = V_{Q}$

$\frac{{dx}_{P}}{dt} = \frac{{dx}_{Q}}{dt}$

$\Rightarrow a + 2 bt = f - 2 t$

$t = \frac{f - a}{2 (1 + b)}$

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