Q. An express train is moving with a velocity $v_{1}$. Its driver finds another train is moving on the same track in the same direction with velocity $v_{2}$. To escape collision, driver applies a retardation $a$ on the train. The minimum time of escaping collision will be
A) $t = \frac{v_{1} - v_{2}}{a}$
B) $t = \frac{v_{1}^{2} - v_{2}^{2}}{2}$
C) None
D) Both
Explanation
(a) As the train are moving in the same direction. So the initial relative speed $(v_{1} - v_{2})$ and by applying retardation final relative speed becomes zero
From $v = u - at \Rightarrow 0 = \left( v_{1} - v_{2} \right) - at \Rightarrow t = \frac{v_{1} - v_{2}}{a}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.