Potential energy functions of a particle

[ramenmeal]

Homework Statement

A single conservative force acting on a particle varies as Fvec = (-Ax + Bx4)i N, where A and B are constants and x is in meters. Accurately round coefficients to three significant figures.
(a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (Use A, B, and x as appropriate.)

(b) Find the change in potential energy and change in kinetic energy as the particle moves from x = 1.80 m to x = 3.40 m. (Use A, B, and x as appropriate.)

Homework Equations

w = f x d

The Attempt at a Solution

ive only attempted part a since i think i will need it to go on to part b.

w = f x d
f = (-Ax + Bx4)
d = x

PE = (-Ax + Bx^4)x = -Ax^2 + Bx^5

 

[LowlyPion]

Since the force is continuously variable over the range of x isn't your U_(x) the integral of the Force F_(x) and not just the product of x and F_(x)?

 

[ramenmeal]

oh yeah.. so should it be

(-1/2)Ax^2 + (1/4)Bx^5 ?

i'm not sure what form my final answer should be.

 

[LowlyPion]

oh yeah.. so should it be

(-1/2)Ax^2 + (1/4)Bx^5 ?

i'm not sure what form my final answer should be.

How about -1/2Ax² + 1/5Bx⁵ instead?