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Question

An express train is moving with a velocity v1. Its driver finds that another train is moving on the same track in the same direction with velocity v2(v1>v2). To escape collision, driver applies break to produce retardation a on the train. The minimum time to avoid collision will be

A
t=v1v2a
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B
t=v21v22a
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C
t=2(v1v2)a
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D
None of the above
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Solution

The correct option is C t=2(v1v2)a

Assuming the frame of reference at 2, we can say:
Relative velocity of 1 with respect to 2: v12=v1v2

We know,
d=ut12at2
At limiting condition, d=0
0=(v1v2)t12at2
12at2=(v1v2)t

t=2(v1v2)a

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