Q

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?

Q 1.     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?

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Given, Diameter of the circular track = $200\ m$

$\therefore$ The circumference of the circular track, $d = 2\pi\frac{D}{2} = 200\pi\ m$

The athlete completes one round of a circular track in 40 s.

$\therefore$ Speed of the athlete = $u = \frac{200\pi\ m}{40\ s} = 5\pi\ ms^{-1}$

In $t = 2\ min\ 20\ s = 140\ s$,

Distance travelled by the athlete = $Speed\times time = (5\pi)\times(140)$

$= 5\times\frac{22}{7}\times140 = 2200\ m$

Also, number of rounds the athlete will complete in $140\ s$ = $\frac{140}{40} = 3.5$

Therefore, the final position of the athlete after $140\ s$ will be diametrically opposite to his initial point.

(3 complete rounds and one half round.)

Hence, displacement of the athlete = magnitude of diameter of the circle = $200\ m$

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