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.