Question

A cyclist starts from the centre $O$ of a circular park of radius one kilometre, reaches the edge $P$ of the park, then cycles along the circumference and returns to the centre along $QO$ as shown in figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is.........

• A. $0,1$
• B. $\frac {\pi+4}{2},0$
• C. $21.4,\frac {\pi+4} {2}$
• D. $0,21.4$

Answer 1

Answer: (D)

$0,21.4$

Answer 2

Since, the initial position of cyclist coincides with final position, so his net displacement is zero.
Average speed $=\frac{\text { total distance travelled }}{\text { total time taken }}$
$=\frac{O P+P Q+Q O}{10} km / min$
$=\frac{1+\frac{\pi}{2} \times 1+1}{10} km / min$
$=\frac{\pi+4}{20} \times 60 km / h$
$=21.4 \,km / h$