Train Crossing a Person: Formula, Rules and Examples
Train Crossing a Person questions use the train’s length and its relative speed with respect to the person. For a stationary person, time equals train length divided by train speed. For a moving person, use the relative speed based on their direction. The key steps are unit conversion, selecting the correct relative speed and applying the distance-time formula.
What Is Train Crossing a Person?
For a train of length L moving at speed v, the crossing time is t = L/v when the person is standing still. If the person moves with speed u, replace v with relative speed: v − u when both move in the same direction, and v + u when they move in opposite directions. Speeds and length must use consistent units.
Train Crossing a Person Formula & Tricks
Important Formulas
Use this when the person is standing still. The distance covered by the train relative to the person is its full length.
Use this when the person and train move in the same direction, where v is train speed and u is person speed.
Use this when the person and train move towards each other.
Convert km/h to m/s when train length is given in metres and time is required in seconds.
Quick Tricks
When a train crosses a person, the front travels from the person’s position until the rear leaves it. Therefore, the distance is the complete length of the train, not half its length.
Subtract speeds for movement in the same direction and add speeds for movement in opposite directions.
If length is in metres and time is required in seconds, convert the speed into metres per second before using t = L/v.
Train Crossing a Person Concepts
Train Crossing a Stationary Person
Use t = L/v. If speed is given in km/h, convert it to m/s when the train length is in metres. For example, a 180 m train moving at 72 km/h has speed 20 m/s, so its crossing time is 180/20 = 9 seconds.
Train and Person Moving in the Same Direction
If the train speed is v and the person’s speed is u, relative speed is v − u, provided v is greater than u. The crossing time is L/(v − u). For a 100 m train at 54 km/h and a person at 18 km/h, relative speed is 36 km/h = 10 m/s, so time is 10 seconds.
Train and Person Moving in Opposite Directions
If the train speed is v and the person’s speed is u, relative speed is v + u. The crossing time is L/(v + u). For a 150 m train at 36 km/h and a person at 9 km/h, relative speed is 45 km/h = 12.5 m/s, so time is 12 seconds.
Finding Train Length or Speed
For a stationary person, relative speed is the train speed. For a moving person, first calculate relative speed using addition or subtraction. Example: if a train crosses a standing person in 8 seconds at 90 km/h, its length is 25 m/s × 8 = 200 m.
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Trains Crossing a Pole or Person
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Train Crossing a Person: Quick Revision
Use the complete train length and the correct relative speed to calculate crossing time.
- For a stationary person, t = L/v.
- For the same direction, relative speed = train speed − person speed.
- For opposite directions, relative speed = train speed + person speed.
- Crossing distance for a person is the full length of the train.
- Use consistent units: convert km/h to m/s by multiplying by 5/18.
- Rearranged forms are L = relative speed × time and relative speed = L/time.
Train Crossing a Person FAQs
What is the train person formula when the person is stationary?
The formula is t = L/v, where L is the train’s length and v is its speed in consistent units.
What relative speed is used when a person walks in the same direction as the train?
Use relative speed = train speed − person speed. Thus, time = train length ÷ (train speed − person speed).
What relative speed is used when a person walks towards the train?
Use relative speed = train speed + person speed because both cover distance towards each other.
A 240 m train moves at 54 km/h. How long does it take to cross a standing person?
54 km/h = 15 m/s. Time = 240/15 = 16 seconds.
A 120 m train moves at 72 km/h and a person walks in the same direction at 18 km/h. Find the crossing time.
Relative speed = 72 − 18 = 54 km/h = 15 m/s. Time = 120/15 = 8 seconds.
Why is the train’s full length used when it crosses a person?
The crossing begins when the front reaches the person and ends when the rear passes the person. Hence, the front travels a distance equal to the complete train length.