Any number of things from a clogged fuel filter, to a faulty ignition component, early 90's hondas are known for their igniters(ingnition control modules) to fail. these are located under the distributor cap.
Bad speed sensors can cause the car to hesitate when accelerating at speeds below 20 mph. The blockage of the air filters can also cause the car to hesitate when accelerating at speeds below 20 mph.
it could be your air filter, you might not be pulling enough air into the engine. it usually costs less than 10 to fix
Lack of propulsion.
A car that hesitates or stumbles when accelerating can have dozens of different problems. Have a knowledgeable person look at it or post a question detailing all symptoms, trouble codes etc.
Slow engine RPM is the main reason a car may be sluggish while accelerating. However, it also could be due to the oil.
Cylinder miss.
"What causes cars to hesitate?
bad wheel bearings
burning lots of fuel to get it going, its an old car.
sounds like a cv joint
Possibly a loose heat shield or other component.
Normally a bent wheel or tire out of balance.