An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?
Answers
Step-by-step explanation:
The distance covered by the athlete is 2200 m and the displacement at the end of 2 min 20s is 200 m.
Answer:
distance = 2200 m, displacement = 200 m
Step-by-step explanation:
Given that the diameter of the circular track is 200 m. So, radius (r) = 200/2 = 100 m
Time taken by an athlete to complete one round is 40 seconds.
Now,
Speed = Distance/Time
Total time athlete moves is 2 min 20 seconds
2 min 20 seconds = 2 × 60 + 20 = 120 + 20 = 140 seconds
Distance covered in one round = Circumference of a circle
Distance covered in one round = 2πr
= 2 × 100 × π
= 200 π
Also, the tme is taken by an athlete to complete one round = 40 seconds.
Number of rounds completed in 140 seconds = 140/40 = 3.5
Distance covered = Number of rounds completed in 140 seconds × circumference
= 3.5 × 2πr
= 3.5 × 2 × 22/7 × 100
= 2200 m
Displacement of an athlete in 2 minutes will be zero because the he will complete 3 rounds and at that time initial and final positions will be same. In later 20 seconds the displacement will be equal to the diameter of the circular track i.e. 200 m.
Displacement = diameter = 200 m
Therefore, the distance covered at the end of 2 min 20 seconds is 2200 m and displacement is 200 m.