An express train is moving with a velocity v1. Its driver finds another train is moving on the same track in the same direction with velocity v2. To escape collision driver applies a retardation a on the train. The minimum time of escaping collision be (a) t = (v1 - v2)/a (b) t = (v1^2 - v2^2)2 (c) None (d) Both

Given

Both the trains are moving in the same direction.

We will first calculate the relative velocity between them

Initial relative velocity will be = v1 – v2

Now, the train gets retarded since the driver applies break. So both the train will move with same velocity i.e = v1 – v2

So, final velocity between them will be v1 – v2 = 0

Applying equation of motion

v = u + at

Here, final relative velocity = 0

Initial relative velocity = u = v1-v2

Now, substituting the values

0 = (v1 – v2) + at

Since the train is retarded, put negative sign with a

0 = (v1 – v2) – at

at = (v1 – v2)

We get,

t = (v1 – v2)/a

Therefore, the correct option is (a)

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