Joe slides along an icy sidewalk -- hard version

Joe, of mass m = 50 kg, 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. What is Joe's acceleration while he is sliding on the sandy patch?
4. What is Joe's velocity when he leaves the sandy patch?