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A particle is moving with a constant speed \(v\) in a circle. What is the magnitude of average velocity after half rotation?
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Verified Answer
The correct answer is:
\(2 \frac{v}{\pi}\)
Hints: 
\(\mathrm{T}=\frac{2 \pi \mathrm{r}}{\mathrm{V}} ; \mathrm{t}_{\mathrm{o}}=\frac{\mathrm{T}}{2}=\frac{\pi \mathrm{r}}{\mathrm{V}} ; \quad \mathrm{V}_{\mathrm{av}}=\frac{2 \mathrm{r}}{\frac{\pi \mathrm{r}}{\mathrm{v}}}=\frac{2 \mathrm{v}}{\pi}\)
\(\mathrm{T}=\frac{2 \pi \mathrm{r}}{\mathrm{V}} ; \mathrm{t}_{\mathrm{o}}=\frac{\mathrm{T}}{2}=\frac{\pi \mathrm{r}}{\mathrm{V}} ; \quad \mathrm{V}_{\mathrm{av}}=\frac{2 \mathrm{r}}{\frac{\pi \mathrm{r}}{\mathrm{v}}}=\frac{2 \mathrm{v}}{\pi}\)
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