# $F=\frac{dp}{dt}$ or $F=ma$? [duplicate]

The second law of Sir Isaac Newton or also known as the fundamental relation of dynamics : $$\vec{F}=m\vec{a}$$ Which can be derived using the definition of the force : $$\vec{F}=\frac{d\vec{p}}{dt}$$ But only if $$m$$ is treated as a constant. What if $$m$$ is not a constant? absolutely we're not having the same result. Then what we must apply $$F=ma$$ or $$F=dp/dt$$ ?

In classical mechanics mass is always a constant. Matter is conserved (it gets a little more complicated in relativity and quantum mechanics but that need not concern us here). When dealing with a question involving "variable mass", for example rocket propulsion, one must divide the mass into the parts which are moving differently. See e.g. Rocket equation. The force accelerating the rocket is $$ma$$, where $$m$$ is variable. It is NOT $$ma + v\dot m$$