Q.
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 point $O$ as shown in figure. If the round trip takes 10 min, the net displacement and average speed of the cyclist (in metre and kilometer per hour) are
A) $0,\ 1$
B) $\frac{\pi + 4}{2},\ 0$
C) $214,\frac{\pi + 4}{2}$
D) $0,\ 21.4$
Explanation
(d) Since, the initial position of cyclist coincides with final position, so his net displacement is zero.
$Average\ speed = \frac{total\ distance\ travelled}{total\ time\ taken}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{OP + PQ + QO}{10}km\ \min^{- 1}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1 + \frac{\pi}{2} \times 1 + 1}{10}km\ \min^{- 1}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{\pi + 4}{20} \times 60\ {kmh}^{- 1} = 21.4\ {kmh}^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.