55
Delayed start (practice)
Textbook: Part 2, lesson 55, pp. 49–51
GoalLagging-motion problems with a starting gap.
New words
starting gap · boshlang‘ich oraliqplan of solution · yechish rejasireverse problem · teskari masaladifference · farq
Explanation
If the objects start S₀ apart and the one in front is faster, the plan is: 1) find the separation speed v₁ − v₂; 2) find how much further apart they get in time t: (v₁ − v₂) × t; 3) add the starting gap: S = S₀ + (v₁ − v₂) × t. In reverse problems we use the same link to find an unknown time or speed. If the one behind is faster, it is catch-up motion and the gap shrinks.
Worked examples
The one in front goes 12 km/h, the one behind 8 km/h, the gap is 5 km: after 4 h it is 5 + (12 − 8) × 4 = 21 km.
The gap grew from 10 km to 40 km in 3 h: the separation speed is (40 − 10) : 3 = 10 km/h.
Class activity
“Catch-up or lagging?”: the teacher says the two speeds and which object is in front; children say whether the gap grows or shrinks and write the matching formula.
Practice
1
A cyclist in front rides at 12 km/h and another, 5 km behind, at 8 km/h in the same direction. How many km apart are they after 4 h?
21
2
Two cars go the same way 10 km apart. The front one goes 80 km/h and the back one 70 km/h. After how many hours are they 40 km apart?
3
3
Two cyclists leave one place in the same direction at 20 and 14 km/h. How many km apart are they after 3 h?
18
4
Two cars leave one place in the same direction. In 3 h the front car gets 45 km ahead. The back car drove at 60 km/h. What was the speed of the front car in km/h?
75