Momentum and kinetic energy

1. Mar 10, 2007

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?

2. Mar 10, 2007

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.

3. Mar 15, 2007

robphy

You may want to look up the more advanced concept of "conjugate momentum" (as seen in discussions of Lagrangian and Hamiltonian mechanics).