Ncert Exercises & Solutions

A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. 4.21. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist?

Fig. 4.21

(a) Since both the start and final positions are the same therefore the net displacement is zero.
(b) Average velocity is defined as the ratio of net displacement and total time taken. Since the net displacement is zero therefore the average velocity is also zero.

A v e r a g e s p e e d = \frac{T o t a l d i s \tan c e}{t i m e t a k e n}

= \frac{O P + a c t u a l d i s \tan c e, P Q + O Q}{10 \times \frac{1}{60} h}

= \frac{1 k m + (\frac{1}{4} \times 2 π \times 1 k m) + 1 k m}{\frac{1}{6} h}

= 21.43 k m / h

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