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This question already has an answer here:

Now this is a very basic question, might look stupid too, but I am not able to understand it. I tried to imagine what momentum really is, and it is the impact of an object. I understood how momentum works, but cannot understand its mathematical formulation. We all know that $p = mv$, but how does this equation work? I mean just by multiplying mass and velocity, how are we able to get this impact? Is there any derivation to this equation?

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marked as duplicate by user36790, Gert, HDE 226868, John Rennie newtonian-mechanics Dec 28 '15 at 15:43

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There's no derivation for it. This is a definition. And the reason we make such a definition is the fact that the sum of momenta in an isolated system is conserved, so it's a very useful quantity to have around. Note that in special relativity if we defined momentum as $p=mv$, then momentum conservation does not hold anymore. So momentum is redefined as $$p=\dfrac{mv}{\sqrt{1-v^2/c^2}}$$ so that the law of conservation of momentum hold again. It's all a matter of definition. Now why it's conserved is another story and it can be proved using Noether's theorem.

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