A train 100 m long is running at a speed of 120 km/h. How many seconds will it take to pass a person standing near the track?

Introduction / Context:
This question focuses on the basic concept of a train passing a stationary observer. It is a direct application of time = distance / speed, where the relevant distance is only the length of the train, since the person is treated as a point on the ground.

Given Data / Assumptions:

• Length of train = 100 m.
• Speed of train = 120 km/h.
• The person is standing still near the track.
• The train moves at constant speed along a straight track.

Concept / Approach:
When a train passes a stationary person, the distance it must cover to pass completely is equal to the length of the train. To find time, we convert the train speed from km/h to m/s and then divide train length by this speed. This yields the crossing time in seconds.

Step-by-Step Solution:
Step 1: Convert train speed from km/h to m/s using 1 km/h = 5/18 m/s. Step 2: Speed in m/s = 120 * 5 / 18 = 600 / 18 = 100 / 3 m/s. Step 3: Distance to be covered relative to the person = length of train = 100 m. Step 4: Use time = distance / speed, so time = 100 / (100 / 3) seconds. Step 5: Simplify: time = 100 * 3 / 100 = 3 seconds.

Verification / Alternative check:
Check by mental calculation. A speed of 100 / 3 m/s is approximately 33.33 m/s. Over 3 seconds, the train covers about 100 m, which exactly matches its length. This confirms that the person will see the entire train pass in 3 seconds from the first to the last coach.

Why Other Options Are Wrong:

• 1 second: At this time, the train covers only about 33.33 m, far less than its length.
• 5 seconds: The train would cover about 166.67 m, more than its actual length.
• 7 seconds: This would give a distance of more than 230 m, which is clearly incorrect for a 100 m train.

Common Pitfalls:
A common error is forgetting to convert km/h to m/s correctly before computing time. Some learners also mistakenly add extra distance such as imaginary platform length even though the question only involves a stationary person. Remember that in person or pole crossing problems, only the train length is relevant for the distance calculation.

Final Answer:
The train will take 3 seconds to pass the person completely.