  # 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?

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Updated on: September 25th, 2023 An athlete completes one round of a circular track of diameter 200 m in 40 s. The distance covered and the displacement at the end of 2 min 20 s will be 2200 m and 200 m respectively. Displacement and distance are two terms that appear to be identical but have different definitions and meanings. Distance refers to the ground covered by an object during motion, whereas displacement refers to how far is an object from the place.

Table of content ## 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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