Question

A train of length $200m$traveling at $30m{s}^{-1}$ overtakes another train of length $300m$ traveling at $20m{s}^{-1}$ Then the time taken by the first train to pass the second is

• A. 10s
• B. 30s
• C. 40s
• D. 50s

Answer 1

The correct option is D

50s

Step 1: Given data:

1. A train of length $200m$ is travelling at $30m{s}^{-1}$
2. Another train of length $300m$ is travelling at $20m{s}^{-1}$.

Relative speed is defined as the speed of a moving body with respect to another.

Now, as both the trains are running in the same direction,

The relative velocity = $\mathrm{velocity}\mathrm{of}\mathrm{first}\mathrm{train}-\mathrm{velocity}\mathrm{of}\mathrm{second}\mathrm{train}$= $30-20=10m{s}^{-1}$

Step 2: Calculating the time taken to overtake the train:

In order to overtake the other train, the first train has to overcome 200 m of its own length and 300 m of the other train,

So, the total distance to be travelled = $200+300=500m$

Also, the relative velocity =$10m/s$

Now we know that,

$Time=\frac{Dis\tan ce}{Speed}$

Therefore, the time taken = $\frac{500}{10}=50sec$

Hence, the correct option is (D).