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} $