Question

A particle is moving along a circular path of radius r with uniform speed V. Then magnitude of average velocity of the particle during the time interval when it moves from A to B is

Moderate

Solution

t = Time of travel $= \frac{S}{V} = \frac{\bar{A B}}{V} = \frac{π r}{2 V}$
d = Displacement = Chord $A B = \sqrt{x^{2} + r^{2}} = \sqrt{2} r$
$∴ |\vec{V_{a v g}}| = \frac{d}{t} = \frac{\sqrt{2} r}{\frac{π r}{2 V}} = \frac{2 \sqrt{2} V}{π}$

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