Trains • Topic 1 of 3

Crossing a Point

A "point" has no length — a pole, a signal post, a standing man, the edge of a platform. To cross it, the train covers exactly its OWN length, because the engine reaches the point first and the last coach clears it last. So time = length ÷ speed, and equivalently length = speed × time. The one habit that separates fast solvers from slow ones is the unit switch: speeds in CAT come in km/h but lengths come in metres, so convert km/h to m/s by multiplying by 5/18 before you divide. A clean check: a train at 72 km/h moves at 72 × 5/18 = 20 m/s, so a 200 m train clears a pole in 200 ÷ 20 = 10 s. Memorise that 18 km/h = 5 m/s, 36 = 10, 54 = 15, 72 = 20, 90 = 25 — those five conversions cover most questions instantly.

✅ Solved examples

1. A 180 m train runs at 54 km/h. How long does it take to cross a telegraph pole?
54 km/h = 54 × 5/18 = 15 m/s. Distance = own length = 180 m. Time = 180 ÷ 15 = 12 s.
2. A train crosses a standing man in 9 seconds at 80 km/h. Find its length.
80 × 5/18 = 200/9 m/s. Length = speed × time = (200/9) × 9 = 200 m.
3. A 150 m train passes a signal post in 7.5 seconds. Find its speed in km/h.
Speed = 150 ÷ 7.5 = 20 m/s. In km/h: 20 × 18/5 = 72 km/h.
4. A 240 m train takes 12 s to pass a pole. How long to pass a man running at the same speed beside the track in the same direction?
Relative speed to a man moving at the train’s own speed is 0, so the train never fully passes him — it takes infinite time. (Trap: equal speeds, same direction, never crosses.)

✏️ Practice — try these, take hints as needed

1. A 200 m train at 72 km/h crosses a pole in how many seconds?
Convert 72 km/h to m/s.
72 × 5/18 = 20 m/s.
Time = 200 ÷ 20.
10 s
2. A train crosses a signal in 8 s at 90 km/h. Find its length.
90 × 5/18 = 25 m/s.
Length = speed × time.
25 × 8.
200 m
3. A 120 m train passes a standing man in 6 s. Find its speed in km/h.
Speed = 120 ÷ 6 m/s.
= 20 m/s.
Multiply by 18/5.
72 km/h
4. A 300 m train runs at 108 km/h. Time to cross a pole?
108 × 5/18 m/s.
= 30 m/s.
300 ÷ 30.
10 s
5. A train passes a pole in 15 s and is 375 m long. Its speed in km/h?
Speed = 375 ÷ 15 m/s.
= 25 m/s.
25 × 18/5.
90 km/h

📝 Topic test — 8 questions

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