question_answer

Which of the following statements is/are correct?

A) Average speed of a particle in a given time period is never less than the magnitude of average velocity.

B) It is possible to have situations in which\[\left| \frac{d\vec{v}}{dt} \right|\ne 0,\]but\[\frac{d|\vec{v}|}{dt}=0\].

C) If the average velocity of a particle is zero in a time interval, then it is possible that the instantaneous velocity is never zero in that interval.

D) All of these.

Correct Answer: D

Solution :

[d]: Average speed\[=\frac{\text{total}\,\text{distance}}{\text{total}\,\text{time}}\] Average velocity \[=\frac{\text{displacement}}{\text{time}}\] \[\because \]distance \[\ge \]displacement                     \[\therefore \]Average speed \[\ge \]average velocity \[\frac{d|\vec{v}|}{dt}=\]tangential acceleration \[\left| \frac{d\vec{v}}{dt} \right|=\]net acceleration         In uniform circular motion,      \[\frac{d|\vec{v}|}{dt}=0,\left| \frac{d\vec{v}}{dt} \right|\ne 0\] In circular motion, from point A to point A again, average velocity = 0 Instantaneous velocity \[\ne 0\] (at any time)