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 us solve the given problem and find out that if an athlete completes 200 m in 40 s, what distance and displacement will he cover at the end of 2 min 20 s.

Explanation:

• Since an athlete completes 200 m in 40 s, after he takes one round of the circular track, we know that the diameter of the circular track is 200 m. So, the radius 'r' = 200/2 = 100 m
• We know that the time taken by the athlete to complete one round of circular track = 40 seconds. Now, the given time = 2 min 20s. So, let us convert it into seconds.
• This will be as follows. (2 × 60) + 20 = 140 seconds (because, 1 minute = 60 seconds)
• Now, we know that when an athlete completes 200 m in 40 s after taking one complete round, we can calculate the number of rounds that he can cover in the given time of 2 min 20 s, using the following formula. Number of rounds covered by the athlete = Total time / Time taken to complete one round = 140/40 = 3.5 rounds
• Distance covered in 1 round = Circumference of the circular track and we know that Circumference of a circle = 2πr
• Thus, the circumference of the circular track = 2 × π × r; where radius (r) = 100 m, and π = 22/7. Circumference of the circular track = 2 × π × r = 2 × 22/7 × 100
• Distance traveled in 140 seconds = Number of rounds covered × Circumference of the track. We know that, the number of rounds covered by the athlete = 3.5; and Circumference of the track = 2 × 22/7 × 10.
• Therefore, Distance traveled in 140 seconds = 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 us 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

Therefore, the distance covered by the athlete to complete a circular track of a diameter 200 m at the end of 2 min 20 seconds is 2200 m and the displacement is 200 m.