Heres what the Michigan SOS says to do when you get a blowout:
If you have a blowout, hold the handle grips firmly, and concentrate on steering and maintaining a straight course. If the front tire blows, shift your weight as far back as you can. If the rear tire blows, do not shift your weight. Do not use either brake. Slowly close the throttle and coast. When your moped is going slowly and it is safe, edge to the side of the road and stop.