An express train is moving with a velocity $v_{1}$ its driver finds another train is moving on the same track in the same direction with velocity $v_{2} .$ To avoid collision driver applies a retardation a on the train. The minimum time of avoiding collision will be

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$t = \frac{v_{1}^{2} - v_{2}^{2}}{2}$

Both A and B

$t = \frac{v_{1} - v_{2}}{a}$

$t = \frac{v_{1}}{a}$

answer is A.

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Detailed Solution

As the train are moving in the same direction so, the initial relative speed $(v_{1} - v_{2})$ and by applying retardation final relative speed becomes zero.

From v = u – at

$\Rightarrow 0 = (v_{1} - v_{2}) - a t$

$\Rightarrow t = (\frac{v_{1} - v_{2}}{a})$

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