Question

A passenger train is moving at $5\text{m}{\text{s}}^{-1}.$ An express train is travelling at $30\text{m}{\text{s}}^{-1},$ on the same track and rear side of the passenger tsrain at some distance. The driver in express train applied brakes to avoid collision. If the retardation due to brakes is $4\text{m}{\text{s}}^{-2},$ the time in which the accident is avoided after the application of brakes is :

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

Answer 1

Answer: (C)

Initial relative velocity of the express trainw.r.t. the passenger train, $u_{ep}=u_e-u_p=30-5=25m{s}^{-1}$ Final relative velocity of the express train w.r.t.the passenger train, $v_{ep}=0$ (because express train comes to rest) From first equation of motion $v_{ep}=u_{ep}-at$ or $0=25-4t$ or $4t=25$ or $t=6.25s$