Where Does the Formula p=mv Originate From in Physics?

[Cheman]

What exactly IS momentum? How do we arrive at the formula "p= mv"? Where does that formula come from - is it purely empirical or is there something more meaningful to it?

Thanks.

 

[dextercioby]

What exactly IS momentum? How do we arrive at the formula "p= mv"? Where does that formula come from - is it purely empirical or is there something more meaningful to it?

Thanks.

It's one of the fundamental concepts in physics.It's introduced purely experimental.It is,alonside position,one variable which describes,at classical level,the physical state of the particle.According to the first Newton's law,an isolated particle has a specific fixed momentum.If it's at rest in an inertial reference system,its momentum is zero.If not,not.Changes of momentum automatically imply that the particle suffered an interraction (and viceversa)described at classical level by forces.Newton's second law should always be stated mathematically by:$\frac{d(m\vec{v})}{dt}$ is equal to the vector sum of all forces acting on the particle.It can be interpreted via "cause-effect logics".
The definiton u gave belongs only to the realm of classical (nonrelativistic)mechanics of pointlike particles in the Newton's approach.
At quantum + relativistic level,it's not valid anymore,because both theories deal with other notion of momentum,the canonical momentum (see Hamilton formalism of classical dynamics).

Regards,

Daniel.