Backfiring on Acceleration

1988 Nissan Sentra Wagon, mileage: 175,000, engine: 1.6L E16. Last week the car, hesitated and then backfired while accelerating quickly making a left turn from a light. The car runs smooth at idle and smooth at 35 MPH or on freeway at a steady speed. At times it runs fine. Today, it ran fine for an hour then started to hesitate and backfire unless I accelerated at a painfully slow rate. I got the car home but the other drivers probably thought I was crazy as they drove around me. But, if I pushed the accellerator down too fast the engine would backfire and I wouldn't get anywhere. What do you think? Throttle position sensor, ignition module or something else? How do you test?