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A body is initially at rest.A net force F acting on it varies with time.Then prove that the body can not remain at rest.

Mathematical Proof:---

Initial velocity = 0

now Force acting was constant or( zero net force)hence acceleration was constant and both were zero hence F= a= 0

now as F varies over time, then differentiation both sides of F=ma w.r.t time we get

df/dt= m da/dt

but, da/dt = v, so we get

df/dt = m*v now since m is constant and Force is not zero therefore velocity is a non zero value which shows theat the body is not at rest. Hope I helped you mate!