Q. The numerical ratio of average velocity to average speed is

A) Always less than one
B) Always equal to one
C) Always more than one
D) Equal to or less than one
Explanation

(d) The average speed
$v_{av} = \frac{length\ of\ path\ ACB}{time\ interval\ \left( t_{2} - t_{1} \right)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
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And average velocity,
$\ \ \ \ \ \ \ \ \ \ \mathbf{v}_{av} = \frac{displacement\ }{time\ interval} = \frac{\mathbf{r}_{2} - \mathbf{r}_{1}}{t_{2} - t_{1}}\ \ \ \ldots(ii)$
But we know that distance is always be greater than or equal to magnitude of displacement. So the average speed will always be greater than or equal to the magnitude of average velocity.
From Eqs. (i) and (ii)
$\ \ \ \ \ \ \ \ \ \ \frac{\mathbf{v}_{av}}{v_{av}} = \frac{displacement\ }{length\ of\ path\ (distance)}\ \leq 1$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.