Train Problems – Perfect Concept Notes

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Train Problems – Perfect Concept Notes

1. Basic Motion Formula

Distance = Speed × Time (Always used in train questions)

2. Speed Conversion

• km/h → m/s: multiply by 5/18


• m/s → km/h: multiply by 18/5

3. Relative Speed

Case 1 - Trains moving in Opposite directions

Relative Speed = Speed₁ + Speed₂ (They move faster towards each other)

Case 2 - Trains moving in Same direction

Relative Speed = Speed₁ – Speed₂ (always bigger speed – smaller speed)

4. Distance Covered While Crossing

Case 3 - Train crosses a pole / tree / signboard

Pole has no length
Distance = Length of train

Case 4 - Train crosses a platform / bridge

Platform has length
Distance = Length of train + Length of platform

Case 5 - Train crosses another train

Both objects have length
Distance = Length₁ + Length₂

5. Time Formula

Time = Distance / Relative Speed

6. Key Idea

All train problems = Length + Speed + Time + Relative Speed

Example

Q: A 100 m train crosses a 200 m platform in 20 s. Find speed.

Total distance covered : Train length + platform length = 100 + 200 = 300 m

Speed : Speed = Distance / Time = 300 / 20 = 15 m/s

Convert m/s to km/h Multiply by 18/5

15 × 18/5
= 3 × 18
= 54 km/h

 Ans = 54 km/h

@. Why multiply by 18/5 ?

1 m/s = ? km/h

Convert meters → kilometers

1 meter = 1/1000 km
So, 1 m/s = 1/1000 km per second

Convert seconds → hours

1 hour = 3600 seconds
So, 1 m/s = (1/1000) km × 3600 per hour

Multiply

1×3600/1000 = 3600/1000 = 36/10 = 18/5

So, 1 m/s = 18/5 km/h