Crossing a Pole & a Platform

🎯 Learning Objective

Account for the train's own length when it crosses points and platforms.

💡 Concept

• Crossing a pole or a standing man (a point): distance = train's own length L
• Crossing a platform, bridge or tunnel: distance = L(train) + L(platform)
• Time = total distance ÷ speed, with speed in m/s
• km/h becomes m/s with × 5/18 — do this before anything else
• Pole time and platform time together reveal both length and speed

🧮 Key Formulas

Pole: t = L/S

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Platform: t = (L + P)/S

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S (m/s) = km/h × 5/18

✏️ Easy Example

Q. A 200 m long train runs at 72 km/h. How long does it take to cross an electric pole?

1. Speed = 72 × 5/18 = 20 m/s
2. Time = 200 ÷ 20

Answer: 10 seconds

🇮🇳 Real-Life Example

At a level crossing you count the seconds while a goods train rumbles past — the gate stays down for exactly (train length ÷ speed) seconds. Longer rake, longer wait.

📝 Exam-Level Example

Q. A 150 m train crosses a 250 m platform in 20 seconds. Find its speed in km/h.

1. Distance = 150 + 250 = 400 m
2. Speed = 400 ÷ 20 = 20 m/s
3. km/h = 20 × 18/5

Answer: 72 km/h

📝 Exam-Level Example

Q. A train crosses a pole in 15 s and a 100 m platform in 25 s. Find the train's length.

1. Extra 100 m took 25 − 15 = 10 s
2. Speed = 100 ÷ 10 = 10 m/s
3. Length = 10 × 15

Answer: 150 m

🪄 Memory Trick

Platform time − pole time = time for the platform's length alone → speed = platform ÷ extra time. Two givens, both unknowns out.

⚠️ Common Mistakes

• ❌ Ignoring the train's length while crossing a platform
• ❌ Dividing metres by a km/h speed without converting

🏆 Exam Tips

• ✅ Standing man = pole = zero length
• ✅ Bridge, tunnel, platform — anything with length gets added

📌 Summary

• Pole → own length only
• Platform → lengths add
• Speed in m/s before dividing
• Extra time × speed = platform length