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(C) Let the initial velocity be $\vec{V}_i = V \hat{i}$ and the final velocity after half a revolution be $\vec{V}_f = -V \hat{i}$.The change in veloc

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$\frac{2 V^2}{\pi r}$

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(C) Let the initial velocity be $\vec{V}_i = V \hat{i}$ and the final velocity after half a revolution be $\vec{V}_f = -V \hat{i}$.The change in velocity is $\Delta \vec{V} = \vec{V}_f - \vec{V}_i = -V \hat{i} - V \hat{i} = -2V \hat{i}$.The magnitude of the change in velocity is $|\Delta \vec{V}| = 2V$.The distance traveled in half a circle is $d = \pi r$.The time taken to complete half a revolution is $t = \frac{d}{V} = \frac{\pi r}{V}$.The average acceleration is defined as $\vec{a}_{avg} = \frac{\Delta \vec{V}}{t}$.Substituting the values,$a_{avg} = \frac{2V}{\frac{\pi r}{V}} = \frac{2V^2}{\pi r}$.

$A$ particle moves around a circular path of radius $r$ with uniform speed $V$. After moving half the circle,the average acceleration of the particle is

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