#### Answer

At x = 5 cm, the force on the particle is 100 N
At x = 15 cm, the force on the particle is 0
At x = 25 cm, the force on the particle is -50 N

#### Work Step by Step

The force $F$ is equal to the negative of the slope of the $U$ versus $x$ graph.
We can find the force on the particle at x = 5 cm. We can use the points (0 cm, 10 J) and (10 cm, 0 J) to find the slope. Therefore;
$F = -\frac{\Delta J}{\Delta x}$
$F = -\frac{0~J - 10~J}{0.10~m-0}$
$F = 100~N$
At x = 5 cm, the force on the particle is 100 N.
At x = 15 cm, the slope of the graph is zero. Therefore, the force on the particle is zero.
We can find the force on the particle at x = 25 cm. We can use the points (20 cm, 0 J) and (40 cm, 10 J) to find the slope.
$F = -\frac{\Delta J}{\Delta x}$
$F = -\frac{10~J - 0~J}{0.40~m-0.20~m}$
$F = -50~N$
At x = 25 cm, the force on the particle is -50 N.