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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) = at + b t² and x_q(t)= ft - t², At what time do the cars have the same velocity?

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

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

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

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

answer is D.

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Detailed Solution

$V_{P} = a + 2 bt$

$V_{Q} = f - 2 t$

$V_{P} = V_{Q} \Rightarrow a + 2 bt = f - 2 t$

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

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