I have recently started to develop games in java using the Slick2D library and am really enjoying it. I have come to a problem where my game need physics and after browsing the web I have decided to use Jbox2D physics engine. Before installing Jbox2D I would just like to be sure that I can use Jbox2D effectively with Slick2D. Just to start off I would just make a plat-former type game with gravity,momentum and friction. It is not a lot of physics and I could probably add this myself but I would like to get familiar with a physics engine in case I move on to games that require more complicated physics. If Jbox2D is not the right physics engine for the job I would be happy to use something else.
This is a somewhat opinionated answer, due to the nature of the question, but I am a developer for slick, and I have used JBox2d, phys2d, libgdx physics2d, and the fizzy wrapper. Of these, Jbox2D appears to be the most fully featured, even though it is difficult to understand. I have been able to run hundreds of polygons without slowing (even on android), and have implemented joints, motors, contact listeners, manually applied forces and impulses, and bodies with multiple shapes (this allows you to have concave bodies, even though concave shapes are not allowed).