At any instant,the velocity and acceleration | vedclass

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Question

(A) The speed of a particle is defined as the magnitude of its velocity,$|v|$.For the speed to increase,the acceleration must act in the same directio

Vedclass · Accepted Answer

$v > 0, a > 0$

Vedclass · Answer

(A) The speed of a particle is defined as the magnitude of its velocity,$|v|$.For the speed to increase,the acceleration must act in the same direction as the velocity.If the velocity $v$ is positive $(v > 0)$,the acceleration $a$ must also be positive $(a > 0)$ to increase the speed.If the velocity $v$ is negative $(v Therefore,the speed increases when the product of velocity and acceleration is positive,i.e.,$v \cdot a > 0$.Among the given options,$v > 0, a > 0$ (Option $A$) and $v < 0, a < 0$ (Option $B$) satisfy this condition. However,typically in such multiple-choice questions,the primary condition is that they have the same sign.

Column-$I$	Column-$II$
$(1)$ Acceleration is positive	$(a)$ Speed of the particle decreases
$(2)$ Acceleration is negative	$(b)$ Speed of the particle increases
	$(c)$ Speed of the particle keeps changing

At any instant,the velocity and acceleration of a particle moving along a straight line are $v$ and $a$. The speed of the particle is increasing if

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Match the items in Column-$I$ with the items in Column-$II$ correctly.

Column-$I$ Column-$II$

$(1)$ Acceleration is positive $(a)$ Speed of the particle decreases

$(2)$ Acceleration is negative $(b)$ Speed of the particle increases

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