Topic: Energy
Concepts: Work, Work-energy theorem

Solution:

The cart initially starts with speed $v_0$ in the negative direction under the influence of a positive force, so negative work $-W_0$ is done on it until it comes to rest. Then the cart reverses direction and has positive work $W_0$ done on it when it returns to the starting point. No net work is done so the cart has the same starting speed $v_0$ in the positive direction.

The maximum speed of the cart is obtained when the maximum positive work is done on it. Since work done is given by the signed area in a $F$–$x$ plot, we see from the graph that this occurs at $x=6\,\mathrm{m}$ with $W=17.5\,\mathrm{J}$. By the work energy theorem,

so the answer is E.