A particle is moving in a circle of radius R with a constant speed v. What is the magnitude of the average acceleration during a time interval equal…

Average acceleration is defined as $\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$. For half a circle, the initial velocity is $\vec{v}_1 = v\hat{i}$ and final velocity is $\vec{v}_2 = -v\hat{i}$. Thus, $|\Delta \vec{v}| = 2v$. The time taken for half a circle is $\Delta t = \frac{\pi R}{v}$. Therefore, $|\vec{a}_{avg}| = \frac{2v}{\pi R / v} = \frac{2v^2}{\pi R}$.