Problem $1-$ A Force $F_x,$ acting on a particle is shown as a function of $x$ in the figure below.

$($a$)$ From the graph, calculate the work done by the force when the particle moves from $x=0m$ to the following values: $x=-4,-3,-2,-1,0,1,2,3,$ and $4m.$

$1$

$($b$)$ Plot the potential energy $U$ vs$,x$ for the range of values of $x$ from $x=-4m$ to $x=4m$ assuming that $U=0$ at $x=0.$ Make sure to label your axes an indicate units for each axis. $($For $U(x)$ vs$,x,U(x)$ should be on the $y-$axis and $x$ should be on the $x-$axis.$)$

Use the grid below, or separate graph paper to make your plot.