To calculate the work done by a force on an object as it is displaced along the $x$-axis, you can use the following principle from physics:

Work-Energy Theorem (for varying forces):

$W = \int_{x_1}^{x_2} F(x) \, dx$ where:

• $W$ is the work done by the force,
• $F(x)$ is the force as a function of position along the $x$-axis,
• $x_1$ and $x_2$ are the initial and final positions (in this case, from 0 m to 3.00 m).

Key Points:

• If the force is constant, the work is calculated as $W = F \cdot d$, where $d$ is the displacement.
• If the force varies with position (as indicated by a graph), you calculate the work by finding the area under the curve of the force-position graph between the limits of displacement.

Steps:

1. Check the shape of the curve: The graph's shape will determine how the work is calculated. If it’s a simple geometric shape like a rectangle, triangle, or trapezoid, you can use basic area formulas.
2. Calculate the area under the curve: The total work done by the force is the area under the graph from $x = 0$ to $x = 3.00 \, \text{m}$.

Please upload the graph of force versus position, and I will calculate the work done based on the area under the curve.

---

Would you like to upload the graph now?

Here are 5 questions to expand on this:

1. What are the units of force on the graph?
2. Is the force positive, negative, or varying along the path?
3. Does the object experience any acceleration during the displacement?
4. Is the graph of force linear or non-linear?
5. Does the object return to its original position after reaching 3.00 m?

Tip: The work done can be negative if the force opposes the displacement direction.