54
Motion with a delayed start
Textbook: Part 2, lesson 54, pp. 46–48
GoalLagging motion: objects going the same way that draw apart.
New words
lagging motion · kechikishli harakatseparation speed · uzoqlashish tezligiin the same direction · bir yo‘nalishdafalling behind · ortda qolish
Explanation
If two objects move in the same direction and the one in front is faster, the one behind falls further and further back – they draw apart. This is called lagging motion. The separation speed is v_sep = v₁ − v₂ (the speed of the one behind is subtracted from the speed of the one in front). If both start from the same place, after time t the distance between them is (v₁ − v₂) × t. For example, if a cyclist in front rides at 18 km/h and a walker behind walks at 5 km/h, the gap grows by 13 km every hour.
Worked examples
From one place in the same direction at 18 and 5 km/h: v_sep = 18 − 5 = 13 km/h; after 3 h, 13 × 3 = 39 km.
Children running from one start line at 6 m/s and 4 m/s are (6 − 4) × 10 = 20 m apart after 10 s.
Class activity
“Fill the table”: in your notebook write, for t = 0, 1, 2, 3, 4 h, how far each object is from the start and the gap between them; see that the gap grows by the same number every hour.
Practice
1
A cyclist at 18 km/h and a walker at 5 km/h leave one place in the same direction. What is the separation speed in km/h?
13
2
How many km apart are this cyclist and walker after 3 h?
39
3
Two children run from one start line in the same direction at 6 m/s and 4 m/s. How many m apart are they after 10 s?
20
4
Two cars leave one place in the same direction at 90 and 70 km/h. After how many hours are they 60 km apart?
3