An express train is moving with a velocity

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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 escape collision, driver applies a retardation a on the train. the minimum time of escaping collision will be

A

$t = \frac{{{v_1} - {v_2}}}{a}$

B

${t_1} = \frac{{v_1^2 - v_2^2}}{2}$

C

None

D

Both

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 escape collision, driver applies a retardation a on the train. the minimum time of escaping collision will be

As the trains 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 $v = u - at$ $⇒$ $0 = ({v_1} - {v_2}) - at$ $⇒$ $t = \frac{{{v_1} - {v_2}}}{a}$