Question

A particle is moving on a circular path of radius $R$ with constant speed $v$ . During motion of the particle from point $A$ to point $B$

• A. Average speed is $v/2$
• B. The magnitude of average velocity is $\frac{v}{\pi }$
• C. The magnitude of average acceleration is $\frac{2v^2}{\pi R}$
• D. Average velocity is zero

Answer 1

Answer: (C)

(a) Average velocity $=\frac{\text{Displacement}}{\text{Total elapsed time}}$
$=\frac{2R}{\frac{\pi R}{v}}=\frac{2v}{\pi }$
(b) Average speed $=\frac{\text{Total distance}}{\text{Total elapsed time}}=\frac{\pi R}{\frac{\pi R}{v}}=v$
(c) Average acceleration
$=\frac{v_f-v_i}{\text{Total elapsed time}}=\frac{2v}{\frac{\pi R}{v}}=\frac{2v^2}{\pi R}$