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## Homework Statement

A force F

_{x}acts on a particle of mass 1.5kg. The force is related to the position x of the particle by the formula F

_{x}= Cx

^{3}, where C = .50. IF x is in maters and F

_{x}is in newtons. (a) What are the SI units of C? (b) Find the work done by this force as the particle moves from x = 3.0m to x = 1.5 m. (c) At x = 3.0m the force points in the opposite direction of the particles velocity (speed is 12m/s) What is its speed at x = 1.5m?

**Ignore (a)**

## Homework Equations

[itex]W = \int F_{x} dx[/itex]

[itex] W = \frac{1}{2}{mv}^{2}_{f} - \frac{1}{2}{mv}^{2}_{i}[/itex]

F

_{x}= Cx

^{3}

## The Attempt at a Solution

Okay, when I solved the problem I used the first equation which gave me -9.5 Joules.

[itex]W = {\int}^{1.5m}_{3.0m} .5x^{3} dx = -9.5 Joules[/itex]

However, when I referenced the solution manual, they placed a negative sign in front of F

_{x}in the equation because the force is "in the opposite direction of the displacement."

[itex]W = {\int}^{1.5m}_{3.0m} -.5x^{3} dx = 9.5 Joules[/itex]

This made no sense to me because the velocity of the particle is, from what I can tell, equal to -12m/s because the force function is always positive. So, it only makes sense to me that the force should be slowing the particle down since the particle is moving in the opposite direction of the force.

Consequently, because of the sign conversion, this throws off the answer to c as well because when I calculated the velocity with the negative work the velocity came out to 11.46m/s however, because the manual claims the work was positive, their result was 13m/s.

Derived Equation:

[itex]\sqrt{\frac{2W+m{v}^{2}_{i}}{m}} = v_f[/itex]

I can not make sense of why the solution manual flipped the sign of the force function.