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)You need to login to perform this action.
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