A boy completes one round of a circular track of diameter 200 m in 30 s. What will be the displacement at the end of 3 minutes and 45 seconds ?
- A.50 m
- B.100 m
- C.200 m
- D.236 m
Correct answer
Explanation
The correct answer is C, 200 m. After 3 minutes 45 seconds the boy has completed seven and a half rounds, so he stands at the point exactly opposite his starting point.
Convert the time: 3 minutes 45 seconds = 180 + 45 = 225 seconds. One round takes 30 seconds, so the number of rounds = 225 ÷ 30 = 7.5. After every full round he is back at the start, so seven rounds give zero displacement. The remaining half round takes him to the other end of the diameter. Displacement is the straight-line distance between the start and the end, which here is the diameter, 200 m. The distance he has covered is much larger: 7.5 × π × 200 ≈ 4,714 m.
A is wrong: 50 m is a quarter of the diameter and matches no position on this track at the end time.
B is wrong: 100 m is the radius, the distance from the centre, not from the starting point.
D is wrong: 236 m is not a possible displacement, since no two points on the circle are more than 200 m apart.
Exam tip: on a circle, displacement after a full round is zero and after half a round equals the diameter.
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