Joe slides along an icy sidewalk -- hard version

Joe slides along a perfectly frictionless icy sidewalk at v = 5 m/s.

However, he hits a patch where some sand adds friction. The patch is L = 3 meters wide. Because the amount of sand changes across the path, the coefficient of kinetic friction changes: it follows the equation

1. What is the friction force on Joe when he is 1 meter into the patch?
2. What is the friction force on Joe when he is 2 meters into the patch?
3. Draw a graph showing "Net Force on Joe" as a function of "distance along patch".
4. What is the work done by friction as Joe moves across the patch?
5. What is Joe's final speed?