An athlete completes one round of a circular track of diameter 200m in 40s. what will be the distance covered and the displacement at the end of 2minutes 20s?
Answers
The diameter of the circular track is 200 m and hence the length of the track would be equal to the circumference of the track, which is equal to pid, where d is the diameter.
Hence, length of the track = pid = 200pi m.
The time taken by the athlete to complete one full circle = 40 s.
Thus, the speed of the athlete = distance covered / time taken = 200pi/40 m/s The diameter of the circular track is 200 m and hence the length of the track would be equal to the circumference of the track, which is equal to pid, where d is the diameter.
Hence, length of the track = pid = 200pi m.
The time taken by the athlete to complete one full circle = 40 s.
Thus, the speed of the athlete = distance covered / time taken = 200pi/40 m/s
= 5pi m/s.
Total time = 2 min and 20 sec.
Since there are 60 seconds in a minute,
the total time = 2 x 60 s + 20 s = 140 s.
The distance covered in 140 s = speed x time = 5pi m/s x 140 s
= 2199.1 m (by using a value of 22/7 for pi, we will get a value of 2200 m).
In 140 s, the athlete will cover 3.5 turns (= 140 s / 40 s/turn = 3.5 turns).
Thus, the athlete would be diametrically opposite to his starting position at the end of 140 s and hence the displacement is the same as the diameter and is equal to 200 m.
Hope this helps.
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