Question

An athlete completes one round of a circular track of diameter 400m in 60s. Calculate
distance covered and the displacement at the end of 2min30s?

Answer 1

Answer:

The diameter of the circular track is given as 200 m. That is, 2r=200 m.

From this radius is calculated as Radius, r = 100 m.

In 40 sec the athlete complete one round. So, in 2 mins and 20 secs, that is, 140 sec the athlete will complete = 140 / 40 = 3.5 (three and a half) rounds.

One round is considered as the circumference of the circular track.

The distance covered in 140 sec = 2πr×3.5=2×3.14×100×3.5=2200 m.

For each complete round the displacement is zero. Therefore for 3 complete rounds, the displacement will be zero.

At the end of his motion, the athlete will be in the diametrically opposite position. That is, displacement = diameter = 200 m.

Hence, the distance covered is 2200 m and the displacement is 200 m.

Answer 2

An athlete completes one round of a circular track of diameter 400m in 60s.

Given that, the diameter is 400 m. So, the radius is 200 m (half of diameter).

As the athlete covers the path in a circular motion. So, the displacement is zero.

Distance cover in one round (during 60 seconds) = 2πr

(2πr = Circumference of the circle)

→ 2 × 22/7 × 200

→ 8800/8

→ 1257.14 m

Distance covered in 1 second (during first or one round) = 1257.14/60 = 20.95 m

We have to find the distance covered and the displacement at the end of 2min 30s.

Displacement is zero (as the path is circular).

Distance covered in 2min 30sec or 150 sec = 20.95 × 150 = 3142.5 m