Distance of particle travels from origin, and maximum speed, picture included

[gap0063]

Homework Statement

A 3.2 kg particle moves along the direction
under the influence of a force described by the
potential energy function U = a k~xk, where
a = 5.48 J/m and x is the position of the
particle in meters measured from the origin
as in Figure.
The total energy of the particle is 18 J.
[PLAIN]http://img828.imageshack.us/img828/2877/problem9.jpg
(a) Determine the magnitude of the distance
that the particle travels from the origin before
reversing direction.
Answer in units of m.
(b)Find the maximum speed of the particle.
Answer in units of m/s.

Homework Equations

Not sure
the only equation I know with distance is $$\Delta$$E_mech=-f_kd

The Attempt at a Solution

So I know the total energy is 18 J
but there is no u
and there is no velocity...maybe i can turn acceleration into velocity?

 

[ehild]

The force is conservative as there is potential energy. In case of conservative forces, the total mechanical energy is conserved. You know the potential energy, U=α|x|. What other energy does the particle have?

ehild

 

[gap0063]

The force is conservative as there is potential energy. In case of conservative forces, the total mechanical energy is conserved. You know the potential energy, U=α|x|. What other energy does the particle have?

ehild

it also has kinetic energy?

so K_i+U_i=K_f+U_f?

 

[ehild]

Yes!

ehild

 

[gap0063]

Yes!

ehild

I'm still confused... what part is U_f and what part is U_i

and I don't know how to calculate kinetic energy without velocity

 

[ehild]

What is the PE at x=0?

ehild