Question

An athlete runs along a circular track of diameter 28m is 8 s what is the displacement and the distance covered by the athlete in 4s

Answer 1

Answer:

2200 m, 200 m

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

Given:

The diameter of the circular track = 28m

The taken by the athlete to complete one round = 8s

To Find:

The displacement and the distance covered by the athlete in 4s

Solution:

The displacement and the distance covered by the athlete in 4s are 28m and 44m respectively.

Since the athlete completes one round in 8 seconds

⇒ In 4 seconds, only half of the track is covered

The displacement is the shortest possible distance between the final and the initial positions.

In the given situation, since the athlete will reach a diametrically opposite point from its starting position,

⇒ The displacement = Length of the diameter

= 28m

The distance covered in 4s = Circumference of the track / 2

= 2πr / 2

= πr

= πd/2

Taking π = 22 / 7

Distance covered = $\frac{22}{7} X \frac{28}{2}$

= 44 m