A particle moves in a circle of radius $R$ with a constant speed $v$. What is the magnitude of the average acceleration of the particle over a time interval of $\frac{\pi R}{2v}$?

1. A.$\frac{2v^2}{\pi R}$
2. B.$\frac{2\sqrt{2}{v}^2}{\pi R}$
3. C.$\frac{v^2}{R}$
4. D.$\frac{\sqrt{2}{v}^2}{\pi R}$