52
Catch-up motion
Textbook: Part 2, lesson 52, pp. 40–42
GoalCatch-up motion: catch-up speed and time to catch up.
New words
catch-up motion · quvlama harakatcatch-up speed · quvish tezligithe one ahead · oldinda ketayotgandifference of speeds · tezliklar farqi
Explanation
If two objects go in the same direction and the one behind is faster, it catches up. Every hour the gap shrinks by v₂ − v₁; this is the catch-up speed. Time to catch up is t = S : (v₂ − v₁). For example, a walker at 5 km/h is 20 km ahead and a cyclist at 15 km/h chases: the catch-up speed is 15 − 5 = 10 km/h and the time is 20 : 10 = 2 h.
Worked examples
80 km/h and 60 km/h: catch-up speed 80 − 60 = 20 km/h.
Gap 45 km, speeds 85 and 70 km/h: 45 : (85 − 70) = 3 h.
Class activity
“Catch-up” diagram: mark the front and back objects on a segment and write how much the gap shrinks each hour.
Practice
1
The car behind goes at 80 km/h and the one ahead at 60 km/h. What is the catch-up speed in km/h?
20
2
A walker at 5 km/h is 20 km ahead. A cyclist at 15 km/h chases. After how many hours does the cyclist catch up?
2
3
The gap is 45 km; the car behind goes 85 km/h and the one ahead 70 km/h. After how many hours does it catch up?
3
4
The gap is 12 km. The cyclist behind rides at 16 km/h and the one ahead at 12 km/h. How many km is the gap after 2 h?
4