If you don't need your path animation to actually be true to some physical system, then you can use the ease channel to create easily (ha ha - get it?) any acceleration, deceleration effect you want.
Eg for a path animation that runs from frames 0-24, and you want rates to change at frame 12
create a path
constrain an object to path
set ease to 0 at frame 0
set ease to 100 at frame 24
go into the channel editor for the ease channel (of the constraint)
Insert keyframe at frame 12. Change ease to to the percentage you want at frame 12. Show bias handles - play with bias handles at frame 12 till the curve looks like you want.