# Momentum and Kinetic Energy

1. Oct 9, 2011

### Joyci116

1. The problem statement, all variables and given/known data
(a) A particle of mass m moves with momentum of magnitude p. Show that the kinetic energy of the particle is given by K=p$^{2}$/2m. (b) Express the magnitude of the particle's momentum in terms of its kinetic energy and mass.

2. Relevant equations
Would the p=mv be needed?

3. The attempt at a solution
I don't know how to get it started. I think I can get it if I can get it started.

Thank you.

2. Oct 9, 2011

### robphy

What is your [starting] expression for kinetic energy?
How is the new expression different from the old one? Any variables missing from one vs the other?

3. Oct 9, 2011

### Joyci116

The equation for kinetic energy is k=.5mV^2 and the new equation is K=p^2/2m. Momentum is missing from the first equation and velocity is missing from the second equation.

4. Oct 9, 2011

### Peter G.

If velocity is missing from the final equation, that means it was substituted in the original equation for K.E. From the equation for momentum (which you listed: p = mv), what is velocity equal to?

5. Oct 9, 2011

K=p^2/2m
K=.5mV^2
p=mv
V=p/m
K=.5m(p/m)^2
K=p^2/2m

6. Oct 9, 2011

7. Oct 9, 2011

### Joyci116

Thank you for the help. :)

8. Oct 9, 2011

No problem