A passenger train is moving at 5 ` ms ^ ( -1 ) ` . An express train is travelling at 30 ` ms ^ ( -1 ) ` , on the same track and rear side of the passenger train at some distance. The driver in express train at some distance. The driver in express train applied brakes in 4 ` ms ^ ( -2 ) ` , the time in which the accident is avoided after the application of brakes is

Options

A. 4.25 s
B. 5.25 s
C. 6.25 s
D. 7.25 s

Answer

C

Explanation

Initial relative velocity of the express train w.r.t the passenger train,
` u _ ( ep ) = u _ e- u _ p = 30 - 5 = 25 m s^( - 1 ) `
Final relative velocity of the express train w.r.t the passenger train,
` v _ (ep) = 0 ` (because express train comes to rest relative to passenger train )
From first equation of motion,
` v_(eq) = u _ ( ep ) - at rArr 0 = 25 - 4t , 4t = 25 `
` rArr t= 6.25 s `