# What is the reason behind the equation $p = mv$? [duplicate]

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?
## marked as duplicate by user36790, Gert, HDE 226868, John Rennie newtonian-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Dec 28 '15 at 15:43
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.