Solve for the motion of the particle x(t)

[lifeonfire]

Homework Statement

A force acting on a particle is given by:
F = ( -(Am)/(y)^3 ) =( -(Am)/(y_0 - x)^3 )
The particle starts at rest at y = y_0.
Solve for the motion of the particle x(t) BY INVOKING ENERGY CONSERVATION

Homework Equations

The Attempt at a Solution

I have no idea how to solve this question using "energy conservation"

I can put F = ma and then integrate to find x(t). But how will I find x(t) with energy conservation. I know U(x) = - integral F(x) dx. But this does not help either.

 

[kuruman]

Can you post the exact statement of the problem? I find it unclear. For example,
1. What are A and m?
2. Is this motion in one or two dimensions?
3. What is the force written in unit vector notation?
4. Your equation implies that y = y_0 - x. What do you think this means?

Please clarify. You need to help us help you.