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Question

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(v2<v1). To escape collision, driver applies a retardation a on the train. The minimum time to escape the collision is


A
(v1v2)a
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B
(v21v22)2
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C
(v2)a
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D
(v1+v2)a
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Solution

The correct option is A (v1v2)a
As the  trains moving in the same direction so the initial relative speed 
(v1v2) and by applying retardation final relative speed become zero.
Initial relative velocity, urel=v1v2 
Final relative velocity, vrel=0 
Relative acceleration, arel=a0=a
Using first equation of motion,
vrel=urel+arelt
0=(v1v2)at
t=(v1v2)a 

Physics

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