Question

Calculate the displacement covered by an athlete by running on a circular path for 50s to complete one round of the path having diameter 42m. Also calculate the distance and displacement after 2 & ½ rounds​

Answer 1

Answer:

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.

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