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.........

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)  (π+4/2),0 (C) 21.4, (π+4 /2) (D) 0,21.4

Tardigrade Admin · Accepted Answer

Since, the initial position of cyclist coincides with final position, so his net displacement is zero.
Average speed

= \frac{total distance travelled}{total time taken}

= \frac{OP + PQ + QO}{10} km / min

= \frac{1 + \frac{π}{2} \times 1 + 1}{10} km / min

= \frac{π + 4}{20} \times 60 km / h

= 21.4 km / h

$0, 1$

$\frac{π + 4}{2}, 0$

$21.4, \frac{π + 4}{2}$

$0, 21.4$

0,1

2π+4​,0

21.4,2π+4​

0,21.4

Since, the initial position of cyclist coincides with final position, so his net displacement is zero. Average speed = total time taken total distance travelled ​ =10OP+PQ+QO​km/min =101+2π​×1+1​km/min =20π+4​×60km/h =21.4km/h

$0, 1$

$\frac{π + 4}{2}, 0$

$21.4, \frac{π + 4}{2}$

$0, 21.4$