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Rest and equilibrium are two states of an object which look similar but are fundamentally different.
Since rest and equilibrium are dependent on reference frames let's understand them from the reference frame of ground.
equilibrium means the absence of a net force on a body which means its "Acceleration" is zero whereas rest means that the " Velocity" of a body is zero.
if we consider a body moving with a constant velocity on a straight road then that body is in equilibrium as the net acceleration is zero but it is not in rest as the velocity is not zero.
thus we can say that every particle at rest (for a considerable amount of time) is in equilibrium but every particle in equilibrium is not at rest.
THANKS FOR READING
-Arvin Gupta
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