A train is running at 40 km/h and crosses a signal pole in 9 seconds. What is the length of the train in metres?

Introduction / Context:
This question focuses on a very basic and important concept in train problems: using speed and time to determine distance, which in this case is simply the length of the train. When a train crosses a pole, only its own length has to pass the point, so distance travelled equals train length.

Given Data / Assumptions:

• Speed of the train = 40 km/h.
• Time taken to cross the pole = 9 seconds.
• The track is straight and level, and the speed is constant.
• When crossing a pole, only the length of the train is relevant.

Concept / Approach:
The fundamental relation is distance = speed * time. However, speed and time must be in compatible units. Since time is given in seconds and the required distance is in metres, we should convert the speed from km/h to m/s before applying the formula. Once we find the distance covered in 9 seconds, that distance is equal to the length of the train.

Step-by-Step Solution:
Convert speed to m/s: 40 km/h = 40 * (5 / 18) m/s. 40 * (5 / 18) = 200 / 18 ≈ 11.11 m/s. Time = 9 s. Distance travelled in 9 s = 11.11 * 9 ≈ 100 m. Therefore, the length of the train is about 100 m.

Verification / Alternative check:
We can quickly check by reversing the calculation. If the train is 100 m long and moves at about 11.11 m/s, then the time to cross a pole is 100 / 11.11 ≈ 9 s, which matches the given time. This confirms that the result is consistent.

Why Other Options Are Wrong:
Lengths like 90 m, 120 m, or 150 m do not match the distance covered by a 40 km/h train in 9 seconds. If the train were 90 m, the time at 11.11 m/s would be about 8.1 s. For 120 m, the time would be about 10.8 s, and for 150 m, about 13.5 s. None of these are equal to 9 seconds.

Common Pitfalls:
The main mistake is not converting km/h to m/s and directly multiplying by seconds, which leads to unrealistically large distances. Another error is thinking that some extra distance is needed when crossing a pole, but in reality only the train length matters in this type of question.

Final Answer:
Hence, the length of the train is 100 m.