What happens when you stop pedaling your bicycle in a flat road?

depending on the type of motion that forced you to stop as well as its own velocity, you would be acted upon by a horizontal force in the direction you were going and then what ever way the other force that acted upon you was going.

For instance if you suddenly stopped because of a horizontal force in the opposite direction that has matched your velocity you would just stop and all of the forces would collide and cancel.

If you had a stick stuck in your spoke of a tire you would be flung horizontally in the direction you were headed.

the equilibrium in ones head will still be trying to move at the speed you were originally going that is why if you suddenly stop after a very long and hard bike ride you might get disoriented for a few seconds, this is why a cool down is always a great idea. Also your muscles have been trying to cope with this new force that has been acting upon it so it will seem after a long ride it is very easy to fall over from leg fatigue.