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A particle, starting from point A, moves with constant speed V along a semicircular path of radius r and finally arrives at diametrically opposite point B. Then its average speed and magnitude of its average velocity are respectively.

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v and $\frac{2 v}{π}$

$\frac{V}{\pi },\,\frac{V}{2\pi }$ $\frac{v}{π} a n d \frac{π v}{2}$

$v a n d \frac{π v}{2}$ $V,\,\frac{4V}{\pi }$

$\frac{v}{π}$ $a n d \frac{v}{2}$ $\frac{V}{2},\,\frac{V}{\pi }$

answer is A.

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Detailed Solution

Average speed = $\frac{D i s \tan c e t r a v e l l e d}{T i m e t a k e n} = \frac{π r}{π r / v} = v$

Average velocity = $\frac{D i s p l a c e m e n t}{T i m e} = \frac{2 r}{π r / v} = \frac{2 v}{π}$

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