A train running at 60 km/h crosses a pole in 12 seconds. What is the length of the train?

Appeared in: AIIMS Delhi NO- 2019

Explanation

The fundamental principle is that when a train crosses a stationary point object like a pole, the distance it travels during the crossing is equal to its own length.
The speed is given in km/h and time in seconds, so the speed must be converted to meters per second (m/s) for consistent units. The conversion factor is multiplying by 5/18.
Calculation: Speed = 60 km/h × (5/18) = 50/3 m/s.
Applying the formula Length = Speed × Time gives: Length = (50/3 m/s) × 12 s = 200 meters.

Option A: This is an incorrect calculation. This result might be obtained if there was an error in the multiplication step, for example, incorrectly calculating (50/3) * 12.
Option B: This is an incorrect calculation. This could arise from mistakenly using 15 m/s as the speed (15 m/s * 12 s = 180 m), which is an incorrect conversion of 60 km/h.
Option D: This is an incorrect calculation. This value might be obtained if the speed was incorrectly calculated as 20 m/s (20 m/s * 12 s = 240 m).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Time, Speed, and Distance: Calculating Train Length as background academic context rather than a clinical decision trigger.
Unit Consistency is Crucial: Always ensure that all units in a calculation are consistent (e.g., meters with seconds, kilometers with hours). The most common error in these problems is failing to convert units correctly.
Object Type Matters: The distance formula changes based on what the train is crossing. For a point object (pole, man), distance = train length. For a length object (platform, bridge), distance = train length + object length.
What if the train crossed a 100m platform? The total distance to be covered would be (Length of Train + 100m). The time taken would be (200m + 100m) / (50/3 m/s) = 300 / (50/3) = 300 * 3 / 50 = 18 seconds.

How to Approach the Question

First, identify the given data from the question: Speed = 60 km/h and Time = 12 seconds.
Recognize that the units are inconsistent (km/h and seconds). Since the options are in meters, the goal is to find the length in meters.
Convert the speed from km/h to m/s using the conversion factor 5/18.
Identify the scenario: The train is crossing a 'pole'. This is a key piece of information which implies the distance traveled is equal to the length of the train.
Apply the core formula: Distance = Speed × Time. In this case, it becomes Length of Train = Speed (in m/s) × Time (in s).
Perform the final calculation and select the option that matches your result.

Concept Tested & Keywords

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Practise the full AIIMS Delhi NO- 2019

Attempt every question from this paper in a timed mock, then review the full solution for each one.