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## Homework Statement

An object is acted on by the force shown in the picture shown below:

What is the final position of the object if its initial position is

*x*= 0.50 m and the work done on it is equal to -0.29 J?

Initial position = Xi = 0.5 m

Work = W = -0.29 J

Force = F

displacement = d

Final position = Xf = ? m

## Homework Equations

W = F(d - Xi) + F(d-d) + F(Xf - d)

W = Fd

## The Attempt at a Solution

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I worked on the first part of this problem, where work was equal to 0.12 J and the initial position was 0.5 m, using this equation:

0.12 = 0.8(0.5 - 0.5) + 0.4(0.75-0.5) + 0.2(Xf - 0.75)

I assumed, since W = Fd, and displacement can't have a negative value, Force would have to have a negative value to get a negative value for Work. Using this logic, I modified the original equation to use a negative Force:

W = -F(d - Xi) - F(d-d) - F(Xf - d)

Using this equation, I went through these steps:

1. Plug in values

-0.29 = -0.8(0.5 - 0.5) - 0.4(0.75-0.5) - 0.2(Xf - 0.75)

2. Reduce

-0.29 = 0 - 0.1 + 0.15 - 0.2Xf

3. Subtract 0.15 and add 0.1 to both sides

-0.34 = -0.2Xf

4. Divide both sides by 0.2

1.7 = Xf

However, the answer I got for the final position (1.7), was incorrect. I'm assuming my initial logic using negative values for force was incorrect, but I'm not sure how else I would solve the problem with a negative work value.

Any help is appreciated. Thanks!

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