Question

The driver of a train moving with speed \(V_1\), observes a train moving at distance \(d\) ahead on the same track slowly in the same direction with a speed \(V_2\). The driver applies breaks to give his train a constant retardation \(a\). If there was no collision between the trains, then

• A. \( d \leq \frac{(V_1 + V_2)^2}{2a} \)
• B. \( d \geq \frac{(V_1 + V_2)^2}{2a} \)
• C. \( d \geq \frac{(V_1 - V_2)^2}{2a} \)
• D. \( d \leq \frac{(V_1 - V_2)^2}{2a} \)

Hint:

When two objects are moving in the same direction, the relative speed and deceleration must be taken into account to calculate the minimum safe distance to avoid collision.

Answer 1

The Correct Option is C

The equation \( d = \frac{(V_1 - V_2)^2}{2a} \) accounts for the relative speed and deceleration between the two trains, ensuring no collision occurs. The distance \(d\) must be at least this value for the trains to avoid collision.