Deriving an acceleration from Potential Energy

[Goatsenator]

Homework Statement

A 4 kg particle moves along the x-axis under the influence of a conservative force. The potential energy is given by U(x) = ax^2 + b, where a = 6J/m^2 and b = 2J. What is the x-component of the acceleration of the particle when it is
at x = 1 m

Homework Equations

deltaU = -W = -mad ?

The Attempt at a Solution

I'm not quite sure what to do here. I thought I could let U(1) = Ufinal and U(0) = Uinitial so then 6 = -W = -Fd = -mad where d = 1 m

I don't think this works because it's a conservative force along the x-axis so acceleration in mad isn't acceleration due to gravity. I'm pretty lost on this one.

 

[ehild]

It is not a constant force, so you need to get the derivative of U with respect to x to find the x component of force:

F_x=-dU/dx.

ehild