Question

An athlete completes a round of a circular track of diameter 200m in 20 s. Calculate (i) the
distance covered by the athlete (ii) the magnitude of the displacement.

Answer 1

Answer:

(i) 200π

(ii) 0

Explanation:

(i) The distance covered is the total length of path transversed, which here is the circumference of the circle.

$Circumference=2\pi r\\=(2\pi)(\frac{200}{2}) =200\pi$

(ii) The displacement is the shortest distance b/w initial point and final point. Here the initial and final points are same, so the shortest length here is 0

Answer 2

Calculate the distance covered and the magnitude of the displacement

Given :-

∵ Diameter = 200 m

∴ Radius = 200/2 = 100 m

(1) To calculate the distance covered by the athlete, we need to calculate the perimeter/circumference of the circular track.

 C = 2πr

     = 2*π*100

    =200π

Let us substitute the value of π

C = 200*3.14 = 628 m.

⇒ The distance covered by the athlete is 200π or 628 m.

(2) Displacement is the shortest path or distance between the initial position and the final position.

Let the initial position of the athlete be A. The athlete completed a round and reached the position from where he started, therefore, the final position of the athlete is also A.

So the displacement is the difference between the final and initial position.

∴ A - A = 0

as now, both the final as well as the initial positions of the athlete is A.

⇒ The magnitude of the displacement is 0.