Make object follow path after animation turned off

I’m trying to make an object follow a path which is quite a simple task but the problem is that at some point during the animation I want to turn the animation off to achieve physical collision.

After turning the animation off the object gets off course instead of continuing and following the given path.

Here is an example:

enter image description here

Let me try to be clearer I want the moving object to maintain it’s direction think of it as train on track when the engine is suddenly stopped working, the train will continue to move on the track. Since the train already developed speed it will take some time until the train will stop completely.
This link might be a hint.

How can I solve this?