Time, Speed & Distance • Topic 3 of 4

Relative Speed

Relative speed is how fast one object moves as seen from another. When two objects move in opposite directions, their relative speed is the SUM of their speeds (the gap closes or opens quickly); when they move in the same direction, it is the DIFFERENCE (the faster slowly reels in the slower). This single idea drives train problems, the "two cars meet" family and overtaking questions. To find when two bodies meet, divide the initial gap by their relative speed. For a train crossing a pole, the distance is just the train’s length; to cross a platform or another train, add the two lengths and divide by the relative speed. Keep units consistent — convert km/h to m/s with 5/18 whenever the gap is in metres and the time in seconds. The reliable habit: decide the direction first, pick sum or difference, then apply distance ÷ relative speed.

✅ Solved examples

1. Two trains, 120 m and 180 m long, move towards each other at 54 km/h and 36 km/h. Time to cross each other?
Relative speed = 90 km/h = 25 m/s. Total length = 300 m ⇒ time = 300/25 = 12 s.
2. A 150 m train at 72 km/h overtakes a man walking at 9 km/h in the same direction. Time to pass him?
Relative speed = 63 km/h = 17.5 m/s. Time = 150/17.5 = 60/7 ≈ 8.57 s.
3. Two cars 200 km apart move towards each other at 60 and 40 km/h. When do they meet?
Closing speed = 100 km/h ⇒ time = 200/100 = 2 hours.
4. A train crosses a 240 m platform in 24 s and a pole in 12 s. Find its length and speed.
Pole: L = 12v. Platform: L + 240 = 24v ⇒ 12v = 240 ⇒ v = 20 m/s; L = 240 m.

✏️ Practice — try these, take hints as needed

1. Two trains 100 m and 140 m long approach each other at 50 and 58 km/h. Time to cross?
Opposite ⇒ add speeds.
Rel = 108 km/h = 30 m/s.
Total length 240 m.
8 s
2. A 180 m train at 90 km/h overtakes a cyclist at 18 km/h (same way). Time to pass?
Same direction ⇒ subtract.
Rel = 72 km/h = 20 m/s.
180/20.
9 s
3. Two buses 300 km apart head towards each other at 70 and 80 km/h. When do they meet?
Add the speeds.
Closing speed 150 km/h.
300/150.
2 hours
4. A train 200 m long crosses a 400 m bridge in 30 s. Find its speed in km/h.
Distance = 200+400.
600/30 = 20 m/s.
×18/5.
72 km/h
5. Two runners on a 400 m circular track at 5 and 3 m/s start together, same direction. Time for the faster to lap the slower once?
Same direction ⇒ subtract.
Rel = 2 m/s.
Gain 400 m at 2 m/s.
200 s

📝 Topic test — 8 questions

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