Why would the Low Coolant light on a 2001 Pontiac Grand Am come on even though coolant level is good for a split second when you first accelerate?

Either the coolant level is low in the recovery tank or the sensor is defective or has a loose connection.

actually most of the time it's the floating magnet in the tank. the magnet goes up and down with the coolant level. If your coolant level is where it should be and it's not overheating then it's something to do with a sensor. but before you run out and buy a new one there a little trick you can do. loosen the tank (it's only one screw that holds it in) and give it a good shake for about 10 seconds. what happens is the floating magnet will get stuck making contact with the sensor and trick it into thinking the coolant is low. 90% of the time this is the problem!!