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Two particles start moving from origin along same straight line such that one moves with constant velocity v and another with constant acceleration a. During the time that elapses before the second catches the first, the greatest distance between the particle is

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$\frac{2 v^{2}}{a}$

$\frac{v^{2}}{a}$

$\frac{v^{2}}{3 a}$

$\frac{v^{2}}{2 a}$

answer is A.

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Detailed Solution

$Let x be the distance between the particles after t seconds. Then$

$x = v t - \frac{1}{2} a t^{2}$

$For x to be maximum$

$\frac{d x}{d t} = 0$

$or t = \frac{v}{a}$

$substituting this value in x we get$

$x = v (\frac{v}{a}) - \frac{1}{2} a {(\frac{v}{a})}^{2}$

$or x = \frac{v^{2}}{2 a}$

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