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A cyclist walks along the boundary of a square field with side 12 m, completing one round in 24 seconds. After walking for 1 minute and 36 seconds, what is the magnitude of the displacement from his starting point?
0 m
12 m
122тАЛm
24 m
0 m
Divide total time by time taken per round to determine the number of complete laps; if the result is an integer, the displacement is zero.
Divide total time by time taken per round to determine the number of complete laps; if the result is an integer, the displacement is zero.
Calculate total time in seconds
1 minute and 36 seconds = 60 seconds + 36 seconds = 96 seconds.
Calculate number of rounds completed
Total time / Time per round = 96 / 24 = 4 full rounds.
Determine final displacement
Since the cyclist completes exactly 4 full rounds, they return to the starting point. Displacement is the straight-line distance from the starting position to the end position. As both points are identical, the displacement is 0 m.
B: 12 m is the distance of one side, not the net displacement after full rounds. C: 12 root 2 m is the length of the diagonal, incorrect for full laps. D: 24 m is the distance covered in one lap, not the net displacement.
A is correct because completing an integer number of rounds (96/24 = 4) brings the cyclist back to the starting point, making the displacement zero.
Always distinguish between total distance covered (path length) and displacement (straight-line distance between start and end). In circular or closed-loop paths, check if the total time is a multiple of the time taken for one full round.