How to find work done by force?

Question

I don't get it. I think it's supposed to be $W = Fd$ and $k = \frac 12 mv^2$... but I don't get which numbers are supposed to go where.

Am I supposed to do $12.5 \times 12$?

Answer 1

Work (in one dimension) is the (signed) area under the force displacement graph.

In the case in which the force is constant with displacement then the work is just force times distance (because then the graph is a rectangle). In this case, the force varies so that probably won't give the correct answer .