Pick the correct statements: - Vidyadip

MCQ

Pick the correct statements:

A
Average speed of a particle in a given time is never less than the magnitude of the average velocity.
B
It is possible to have a situation in which $\Big|\frac{\text{d}\vec{\text{v}}}{\text{dt}}\Big|\neq0$ but $\frac{\text{d}}{\text{dt}}|\vec{\text{v}}|=0.$
C
The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.
✓
All of the above

✓

Answer

Correct option: D.

All of the above

Average speed of a particle in a given time is never less than the magnitude of the average velocity.
It is possible to have a situation in which $\Big|\frac{\text{d}\vec{\text{v}}}{\text{dt}}\Big|\neq0$ but $\frac{\text{d}}{\text{dt}}|\vec{\text{v}}|=0.$
The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.

Example, the motion of a particle on a circular track with a constant speed.
Average velocity $=\frac{\text{Displacement}}{\text{Total time}}$
$\text{Displacement}\leq\text{Distance}$
$\therefore\text{Average velocrty}\leq\text{Average speed}$
In uniform circular motion, speed is constant but velocity is not.
$\text{i.e.},\Big|\frac{\text{d}\vec{\text{v}}}{\text{dt}}\Big|\neq0$ but $\frac{\text{d}}{\text{dt}}=|\vec{\text{v}}|=0$ which proves case $(b)$

In one complete circle of uniform motion, average velocity is zero. Instantaneous velocity is never zero in the interval.

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