Trains Sums Formula Sheet

#	📌 Category	📝 Formula / Rule
1	🔄 km/hr → m/s	$a \text{ km/hr} = a \times \dfrac{5}{18} \text{ m/s}$
2	🔄 m/s → km/hr	$a \text{ m/s} = a \times \dfrac{18}{5} \text{ km/hr}$
3	⏱️ Time Formula	$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}}$ Time=SpeedDistance
4	📏 Train passing a pole / standing man / signal post	Distance covered = Length of train = l metres
5	📏 Train passing a stationary object of length b*	Distance covered = (l + b) metres
6	➡️ Relative Speed — Same Direction (speeds u & v, u > v)	Relative Speed = (u − v) m/s
7	↔️ Relative Speed — Opposite Directions (speeds u & v)	Relative Speed = (u + v) m/s
8	↔️ Two trains cross — Opposite Directions (lengths a, b; speeds u, v)	$\text{Time} = \dfrac{(a + b)}{(u + v)} \text{ sec}$
9	➡️ Two trains cross — Same Direction (lengths a, b; speeds u > v)	$\text{Time} = \dfrac{(a + b)}{(u – v)} \text{ sec}$
10	🔁 Trains from opposite ends A & B — Speed Ratio (after crossing, take a sec & b sec to reach B & A)	$\dfrac{\text{Speed of A}}{\text{Speed of B}} = \sqrt{\dfrac{b}{a}}$

💡 Note	Detail
✅ Always convert speed to same unit before applying formulas	km/hr ↔ m/s using ×5/18 or ×18/5
✅ For a train crossing a bridge/platform	Add both lengths: Train length + Bridge/Platform length
✅ For a train crossing a pole/person	Use only Train length (person/pole has negligible length)
✅ Same direction → subtract speeds	Slower train appears almost stationary to faster one
✅ Opposite direction → add speeds	They approach each other quickly

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