Answer
See the detailed answer below.
Work Step by Step
We have 3 stages of motion which are from $x=0$ cm to $x=10$ cm, from $x=10$ cm to $x=20$ cm, and from $x=20$ cm to $x=40$ cm.
It is obvious that the three stages are having three constant slopes since they are represented by a straight line.
So we need to find the slope of each stage:
$${\rm Slope}=\dfrac{\Delta U}{\Delta x}$$
So, we need to find the slope of each stage.
$${\rm Slope}_1=\dfrac{ U_f-U_i}{ x_f-x_i}=\dfrac{0-10}{0.10-0}=\bf -100\;\rm J/m$$
$${\rm Slope}_2=\dfrac{ U_f-U_i}{ x_f-x_i}=\dfrac{0-0}{0.20-0.10}=\bf -0\;\rm J/m$$
$${\rm Slope}_3=\dfrac{ U_f-U_i}{ x_f-x_i}=\dfrac{10-0}{0.40-0.20}=\bf 50\;\rm J/m$$
We know that the force is given by
$$F_x=\dfrac{-dU}{dx}=-{\rm Slope}$$
Thus,
- At $x=5$ cm, which is in the first stage, the force is
$$F_x=-{\rm Slope}_1=-(-100)=\color{red}{\bf 100}\;\rm N$$
- At $x=15$ cm, which is in the second stage, the force is
$$F_x=-{\rm Slope}_2=-(0)=\color{red}{\bf 0}\;\rm N$$
- At $x=25$ cm, which is in the third stage, the force is
$$F_x=-{\rm Slope}_3=-(50)=\color{red}{\bf 50}\;\rm N$$
- At $x=35$ cm, which is in the third stage, the force is
$$F_x=-{\rm Slope}_3=-(50)=\color{red}{\bf 50}\;\rm N$$
