Sounds like if you just make your pieces into active rigid bodies, you’ll get what you want. There are a few ways to do that.
I would just make them nCloth objects (nCloth can be rigid, it doesn’t need to deform like fabric) and then throw either a radial field on them at the center of the exploded object (where you want the pieces to explode from) or if you want the pieces to be a bit more unique in their movement, you can use a newton field (negative magnitude value) and give each piece a different mass (radial field won’t care about mass). You probably want to keep “attenuation” rather high so the “push” gets weaker as the pieces get further from the point where the field is (origin of explosion).
If you haven’t used the nSolver before, the solver node (probably will be named “nucleus1”) has a built in gravity which is on by default. Also, it has a built in ground plane which you can enable if you wish.
Hope that helps!