I did whole mini game like this. I used path and attached model of carriage to it. Then it is just settin key frames for rotation and speed. There was a lot of graph editor work though.
The biggest problem was that if some things went wrong, I had to redo whole sequence. So plan ahead what elements you need. Fx I learned that speed had to be animated first, then rotations of carriage and then details. If you do speed after any other key frames, the sequence will be ruined because of speed inaccuracies.
That's what I created: https://lubyslaurynas.com/roller_field.html