How is kinetic energy related to momentum in terms of velocity?

[xiankai]

if you differentiate kinetic energy wrt. to velocity, you will get momentum as the result.

what i wanted to ask is that, how can this physically explained? that kinetic energy can be viewed as the rate of change of momentum for a change in velocity? is there any analogy?

 

[StatMechGuy]

The derivation of energy conservation is where this comes from. You start with Newton's laws, then integrate basically with respect to the velocity, and what comes out is the kinetic energy on the ma side and potential energy on the other side. That's why it comes out that way.

 

[robphy]

You may want to look up the more advanced concept of "http://www.google.com/search?q=conjugate+momentum+lagrangian+hamiltonian"" (as seen in discussions of Lagrangian and Hamiltonian mechanics).