Which of the following statements are correct | vedclass

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Question

(A) Average speed is defined as $	ext{Total Distance} / 	ext{Total Time}$,while the magnitude of average velocity is $	ext{Total Displacement} /

Vedclass · Accepted Answer

$a, b, c$

Vedclass · Answer

(A) Average speed is defined as $	ext{Total Distance} / 	ext{Total Time}$,while the magnitude of average velocity is $	ext{Total Displacement} / 	ext{Total Time}$. Since $	ext{Distance} \geq |	ext{Displacement}|$,statement $(a)$ is correct.$(b)$ $|d\vec{v}/dt| 
eq 0$ implies non-zero acceleration (e.g.,centripetal acceleration in uniform circular motion). $d/dt|\vec{v}| = 0$ implies the speed is constant. This is possible in uniform circular motion,so $(b)$ is correct.$(c)$ If a particle moves in a closed path (like a circle),the total displacement is zero,making average velocity zero,even if the instantaneous velocity is never zero. So,$(c)$ is correct.$(d)$ For motion in a straight line,if the average velocity is zero,the displacement is zero. For a continuous function,if the displacement is zero,the velocity must be zero at some point in the interval (by Rolle's Theorem). Thus,$(d)$ is incorrect.

Column $I$	Column $II$
$(A)$ Change in velocity	$(p)$ $-5/3\,SI \text{ unit}$
$(B)$ Average acceleration	$(q)$ $-20\,SI \text{ unit}$
$(C)$ Total displacement	$(r)$ $-10\,SI \text{ unit}$
$(D)$ Acceleration at $t=3\,s$	$(s)$ $-5\,SI \text{ unit}$

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