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 min 20 s?

Distance and Dispacement

Displacement and distance are both measurements of an object’s motion, but they have different implications.

• Distance is the total length of a path that an object has taken while moving. It is always positive and a scalar quantity. Distance solely takes into account the size of the path travelled and is direction-independent.
• Displacement describes the shift in an object’s location from its starting position to its ultimate position. It has both magnitude and direction, making it a vector quantity. The shortest direct path between an object’s original and final positions is taken into account when measuring displacement.

Solution

Given that:

Diameter of circular track = 200 m

Radius r = 200/2 = 100 m

Time taken by an athlete to complete 1 round = 40 seconds

Speed = Distance/ Time

Total time an athlete moves = 2 min 20 s

2 min 20 s = 2 x 60 + 20 = 140 seconds

Distance covered in 1 round = Circumference of the circle = 2πr

= 2 x 100 x π

= 200π

Time taken by an athlete to complete 1 round = 40 s

Number of rounds completed in 140s = 140/40

= 3.5

Distance covered = 3.5 x circumference

= 3.5 x 2πr

= 3.5 x 2 x 3.14 x 100

= 2198 = 2200 m (approx)

The displacement in 2 mins i.e. 120 s is zero as the athlete will complete 3 rounds and at that time, the initial and final position will remain the same

In the next 20s, displacement is equal to the diameter of a circular track, i.e. 200m

Displacement will be 200m as it returns to its initial position

Therefore, the distance covered will be 2200 m and the displacement at the end of 2min 20s is 200 m.

Summary:

An athlete completes one round of a circular track of diameter 200m in the 40s. What will be the distance covered and the displacement at the end of 2min 20s?

An athlete completes one round of a circular track of diameter 200m in the 40s. The distance covered will be 2200 m and the displacement at the end of 2min 20s is 200 m.

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