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 PQ circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in kilometre and kilometer per hour) is

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0, 2( $π + 4$ )

$\frac{π + 4}{2}, 0$

$21.4, \frac{π + 4}{2}$

0, 3( $π + 4$ )

answer is D.

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Detailed Solution

Net displacement of the cyclist = zero
Since the initial position coincides with the final position.
Average speed of the cyclist = $\frac{Total distance travelled}{Total time taken}$

= $\frac{OP + PQ + QO}{10} km \min^{- 1} = \frac{1 + \frac{π}{2} \times 1 + 1}{10} km \min^{- 1}$

= $3 (π + 4) km / hr$

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