What does p = mv really mean? For example, why is there a physical law based upon the product of mass and velocity? Why does a human made operation, multiplication, give a quantity called momentum? If we define momentum as the product of m and v, why can't we define by some other operation, like division? For example, if m = 5, and v = 3, what is it about adding 5 to itself three times that gives this quantity called momentum in 15 kg m/s?