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. 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. $t_{1} = \frac{v_{1}^{2} - v_{2}^{2}}{2}$
• C. None
• D. Both

Answer 1

Answer: (A)

$t = \frac{v_{1} - v_{2}}{a}$

Answer 2

As the trains 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 $v = u - at$ ⇒ $0 = (v_{1} - v_{2}) - at$ ⇒ $t = \frac{v_{1} - v_{2}}{a}$