# Momentum and Kinetic Energy

## Homework Statement

(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.

## Homework Equations

Would the p=mv be needed?

## 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.

## Answers and Replies

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robphy
Homework Helper
Gold Member
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?

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.

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?

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

Thank you for the help. :)

No problem