Two cars are travelling towards each other at speed of 20 m s-1 each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s-2. The distance between them when they come to rest is :
- 25 m
- 100 m
- 50 m
- 200 m
Answer
(2) 100 m
Solution
Look at the motion of one car relative to the other.
Relative speed urel = 20 + 20 = 40 m s-1 and relative retardation arel = 2 + 2 = 4 m s-2; both cars stop at the same instant (after 10 s), so the relative velocity also becomes zero then.
vrel2 = urel2 - 2arels 0 = 402 - 2 4 s s = 200 m
So the gap closes by 200 m, and the distance left between them = 300 - 200 = 100 m, so (2) is correct.
(4): 200 m is the gap closed, not the gap left, so (4) is wrong; (1) 25 m and (3) 50 m do not fit, so they are wrong.
Answer: (2)