A cyclist starts from the centre O of a circular park of radius 1 km,

1.	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. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist?
Answer» (a) Since the cyclist returns to the starting point, his net displacement is zero. (b) The average velocity =\(\frac{Net\,displacement}{Time\,taken} =0\) (c) Average speed = \(\frac{\textit{Length of the path}}{\textit{Time taken}}\) =\(\frac{Op+arcPQ+QO}{10min}\) \(= \frac{1 \mathrm{km}+1/{4} \times 2 \pi \times 1 \mathrm{km}+1\mathrm{km}}{1 / 6 \mathrm{hour}} = 21.4 km / hour.\)

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. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist?

Answer»

(a) Since the cyclist returns to the starting point, his net displacement is zero.

(b) The average velocity

=\(\frac{Net\,displacement}{Time\,taken} =0\)

=\(\frac{Op+arcPQ+QO}{10min}\)

\(= \frac{1 \mathrm{km}+1/{4} \times 2 \pi \times 1 \mathrm{km}+1\mathrm{km}}{1 / 6 \mathrm{hour}} = 21.4 km / hour.\)