2001 Dodge Caravan Problem accelerating when first started

2001 Dodge Caravan SE is having acceleration problems when first started. When I start the van, it accelerates fine to about 20 mph and then as I push the accelerator more there is no more acceleration and rpms don't rise. It might get a little jumpy (i.E. Accelerate very briefly and drop back down). It does this for about the first 1/4 to 1/2 mile and then will work fine, even after stopping at intersections and reaccelerating.

This just started about 2 months ago. For a while it was also spewing black specks when first started (I was told this was unburnt fuel and the engine was misfiring.) A tune up took care of the black stuff but the acceleration still seems to be there along with poor mileage.

It typically only does this after sitting for at least a few hours and to me feels like what I would imagine it would be like if it isn't getting fuel properly when I try to accelerate.