Problems on Trains
Master the logic of self-length and relative distance. Learn how to solve complex crossing scenarios involving platforms, bridges, and moving observers.
1. The Fundamental Crossing Law
Distance covered during crossing is the SUM of lengths involved.
- Crossing a Pole/Man: Distance = Length of Train (L_1).
- Crossing a Platform/Bridge: Distance = Length of Train + Length of Platform (L_1 + L_2).
Example:
Q: A 200m train crosses a pole in 10s. Speed?
Solution: Speed = 20010 = 20 m/s = 72 kmph.
2. Relative Speed in Trains
When two trains cross each other.
- Total Distance: ALWAYS L_1 + L_2 (Lengths never subtract).
- Relative Speed (Opposite): S_1 + S_2.
- Relative Speed (Same): S_1 - S_2.
Example:
Q: Two trains (150m, 250m) at 40 kmph and 50 kmph (Opposite). Time?
Solution: Total Dist = 400m. Rel Speed = 90 kmph = 25 m/s.
Time = 40025 = 16 sec.
Time = 40025 = 16 sec.
3. Point Observer in a Moving Train
When a faster train crosses a Man sitting in a slower train.
- The Model: Treat the Man as a point object moving at the speed of the slower train.
- Logic: Distance = ONLY the length of the Faster Train (L_{fast}).
- The length of the slower train is IRRELEVANT.
Example:
Q: Fast train (200m) crosses a man in slow train in 10s. Rel Speed?
Solution: Distance = 200m. Time = 10s.
Rel Speed = 20010 = 20 m/s.
Rel Speed = 20010 = 20 m/s.
4. Unit Conversion Sniper
Trains usually use 'kmph' for speed and 'meters' for length. Convert immediately.
- kmph to m/s: Multiply by 518.
- m/s to kmph: Multiply by 185.
Example:
Q: Convert 54 kmph to m/s.
Solution: 54 × 518 = 3 × 5 = 15 m/s.
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