A particle moves in a circle of radius $R$ with a constant speed $v$. If the time taken for one revo

Question

A particle moves in a circle of radius $R$ with a constant speed $v$. If the time taken for one revolution is $T$, what is the magnitude of the average acceleration of the particle over half a revolution?

Professor PC Thomas Classes · Answer

Average acceleration $\vec{a}_{avg} = \frac{\Delta\vec{v}}{\Delta t}$. Over half a revolution, the velocity vector completely reverses direction, so $|\Delta\vec{v}| = |-v - v| = 2v$. The time taken is $\Delta t = \frac{T}{2}$. Therefore, $|\vec{a}_{avg}| = \frac{2v}{T/2} = \frac{4v}{T}$.