Determine the work done to move the particle

[Bones]

Homework Statement

The net force exerted on a particle acts in the positive x direction. Its magnitude increases linearly from zero at x = 0, to 284 N at x = 3.0 m. It remains constant at 284 N from x = 3.0 m to x = 7.0 m and then decreases linearly to zero at point A where x = 9.2 m. Determine the work done to move the particle from x = 0 to x = 9.2 m by graphically determining the area under the F versus x graph.

Homework Equations

The Attempt at a Solution

I drew the graph and it looks like a trapezoid. I am not sure where to go from here.

 

[LowlyPion]

Homework Statement

The net force exerted on a particle acts in the positive x direction. Its magnitude increases linearly from zero at x = 0, to 284 N at x = 3.0 m. It remains constant at 284 N from x = 3.0 m to x = 7.0 m and then decreases linearly to zero at point A where x = 9.2 m. Determine the work done to move the particle from x = 0 to x = 9.2 m by graphically determining the area under the F versus x graph.

Homework Equations

The Attempt at a Solution

I drew the graph and it looks like a trapezoid. I am not sure where to go from here.

Welcome to PF.

What is the area then of your trapezoid?

Isn't Work the product of the Force multiplied by the distance over which it acts?
So when Force is a function of distance isn't it:

$$Work = \int F_{(x)} dx$$

And this can be found graphically by measuring the area under the graph.

 

[Bones]

Yeah, I figured it out. It just helps sometimes to find a good example for guidelines. Thanks ;)