Answer
The work done by the force is $~~25.0~J$
Work Step by Step
To find the work done, we can calculate the area under the force versus position curve.
This area can be divided into three parts, including a rectangle (0 to 2 m), a triangle, (2 m to 4 m), and a triangle (6 m to 8 m).
We can find each area separately:
$A_1 = (10.0~N)(2~m) = 20.0~J$
$A_2 = \frac{1}{2}(10.0~N)(2~m) = 10.0~J$
$A_3 = \frac{1}{2}(-5.0~N)(2~m) = -5.0~J$
We can find the work done by the force:
$W = 20.0~J+10.0~J-5.0~J = 25.0~J$
The work done by the force is $~~25.0~J$.
