A passenger sitting in a train A moving at 90 km / h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km / h, then length of train B is:

Solution

Physics sir · 4 steps

Sit in train A: then train B rushes past you at 90 + 54 km/h, and that speed sweeps its length.

1. Relative speed. The trains move in opposite directions, so their speeds add as seen by the passenger. That gives 90 + 54 = 144 km/h.
2. Convert units. Multiply by 5/18 to get metres per second: 144 × 5/18 = 40 m/s.
3. Length covered. The passenger is a point. In 8 s, the whole length of B passes that point at the relative speed.

   L_B = vᵣₑₗ × t = 40 m/s × 8 s = 320 m

4. So. The length of train B is 320 m, option (d).

The idea to keep. Opposite directions: add the speeds. Same direction: subtract them. A point observer sees only the other train's length go past, never their own.

Answer from the NTA final answer key. Solution by PrepWiser.