An athlete completes one round of a circular track of a diameter of 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 min 20s?
Distance is defined as a complete path traveled by an object. Displacement is defined as the shortest distance between two points.
Answer: The distance covered by the athlete is 2200 m and the displacement at the end of 2 min 20s is 200 m.
Let's understand the given problem.
Given : Diameter of circular track = 200 m
Radius 'r' = 200/2 = 100 m
Time taken by the athlete to complete one round of circular track = 40 seconds
Now, time = 2 min 20s = (2 × 60) + 20 = 140 seconds (Since, 1 minute = 60 seconds)
Number of rounds covered by the athlete = Total time / Time taken to complete one round
= 140/40 = 3.5
Distance covered in 1 round = Circumference of the circular track
Thus, the circumference of the circular track = 2 × 22/7 × 100
Distance traveled in 140 seconds = Number of rounds covered × Circumference of the track
= 3.5 × 2 × 22/7 × 100
= 0.5 × 2 × 22 × 100
Thus, the distance covered by the athlete is = 2200 m
Now, to calculate the displacement let's observe the following diagram.
Let the athlete start from point A and reach point B after 140 seconds.
Thus, the displacement will be equal to the length of the line segment AB.
Length of AB = Diameter of the circle = 200 m
Thus, the displacement of the athlete is 200 m