A locomotive driver travelling at 72 km/hr finds a signal 210 metres ahead of him indicating that he should stop. He instantly applies brakes to stop the train. The train retards uniformly and stops 10 metres before the signal post. What time did he take to stop the train?

Options

A. 5 seconds
B. 10 seconds
C. 15 seconds
D. 20 seconds

Answer

To solve the problem step by step, we will follow these calculations:

1. **Identify the initial speed of the train**:
The train is traveling at a speed of 72 km/hr.

2. **Convert the speed from km/hr to m/s**:
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).
\[ \text{Speed in m/s} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

3. **Determine the distance the train needs to stop**:
The signal is 210 meters ahead, but the train stops 10 meters before the signal. Therefore, the distance to stop is:
\[ \text{Distance to stop} = 210 - 10 = 200 \text{ meters} \]

4. **Calculate the time taken to stop**:
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
We can substitute the values we have:
\[ \text{Time} = \frac{200 \text{ meters}}{20 \text{ m/s}} = 10 \text{ seconds} \]

5. **Conclusion**:
The time taken for the train to stop is 10 seconds.