1. An athlete completes one round of a circular track of diameter 200 min 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?
Answers
Answer:
Explanation:
Distance and displacement are two terms that appear to be identical but have quite different meanings and definitions. The term “distance” relates to how much ground an object has covered during its motion, whereas “displacement” refers to how far out of place is an object.
Given parameters
The diameter of the circular track = 200 m
Radius (r) = 200/2
r = 100 m
Time is taken by an athlete to complete one round = 40 seconds.
Displacement = ??
Speed = Distance/Time
Total time athlete moves – 2 min 20 seconds
2 min 20 seconds = 2 × 60 + 20
2 min 20 seconds = 140 seconds
Find the distance covered in one round
Distance covered in one round = Circumference of a circle.
Distance covered in one round = 2πr
Distance covered in one round = 2 × 100 × π
Distance covered in one round = 200π
Time is taken by an athlete to complete one round = 40 seconds.
Number of rounds completed in 140s = 140/40
Number of rounds completed in 140s = 3.5
Distance covered = 3.5 × circumference
Distance covered = 3.5 × 2πr
Distance covered = 3.5 × 2 × 3.14 × 100
Distance covered = 2198 ≈ 2200 m
Displacement in 2 mins that is 120 s will be zero because the athlete will complete 3 rounds and at that time initial position and final position will be the same.
But, later the next 20 s the displacement will be equal to the diameter of the circular track which is 200 m.
Hence, the distance covered at the end of 2 min 20 seconds is 2200 m or 22 km.
And displacement is 200 m as it returns to the initial position.