What happens:
A minecart that runs out of track and has no ground directly under it will slow down at a fast rate.

What I think should happen:
A minecart that runs out of track and has no ground directly under it should not lose any (or much) of its horizontal speed. An airborn minecart should only slow down quickly if it enters water or lava while falling.

How to observe:
Build straight line of blocks floating high up in the air and place powered rails on top. Use either a redstone torch, redstone block, or a lever to give the rails constant power. Then, put a minecart on the track and push it so that it starts moving. Once the minecart runs out of track on the floating blocks you created, it will start to fall down. At the same time, it will begin to quickly stop moving forward (as if the air was dense like water).

Code analysis by marcono1234 can be found in this comment