### Chapter - 1 Motion

Q
##### Motion

Question:

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 minutes 20 s?

Diameter of a circular track, $d = 200\ m$

Radius of the track,  $r = \frac{d}{2}=100\ m$

Circumference  $=2 \pi r = 2 \pi (100) = 200 \pi$

In 40 s, the given athlete covers a distance of $200 \pi \ m$.

In 1 s, the given athlete covers a distance $= \frac{200 \pi}{40}\ m$

The athlete runs for 2 minutes 20 s = 140 s

Total distance covered in 140 s $= \frac{200 \times 22}{40 \times 7} \times 140 = 2198 \ m$

The athlete covers one round of the circular track in 40 s. This means that after every 40 s, the athlete comes back to his original position. Hence, in 140 s he had completed 3 rounds of the circular track and is taking the fourth round.

He takes 3 rounds in $40 \times 3 = 120$ s. Thus, after 120 s his displacement is zero. Then, the net displacement of the athlete is in 20 s only. In this interval of time, he moves at the opposite end of the initial position. Since displacement is equal to the shortest distance between the initial and final position of the athlete, displacement of the athlete will be equal to the diameter of the circular track.

$\therefore$ Displacement of the athlete  = 200 m.

So, the distance covered by the athlete in 2 min 20 sec is 2198 m and his displacement is 200 m.

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