When was the last time the engine was tuned up? No, not just plugs, but a full tune up! The whole nine yards! Any part of the secondary ignition will do this including the ignition coil or coils! This sounds like a classic ignition misfire! They usually go bad under a load like under acceleration, but can be noticeable at any time. It is very important to have your engine equipped with good tune up parts or you may be causing damage to other components of you car like the catalytic converter which can be expensive!
Ignition misfire causes by any bad tune up part and or ignition coil or coils.
Bad spark plugs, spark plug wires and cap and rotor (if equipped)
Wrong tune up parts spark plug, wires etc...
The quickest way to check the ignition components, is by looking closely for leaking secondary voltage. Visual look at all the tune up parts to see if you can see any sparks coming from any of the wires or coil (or coils) when the vehicle is running. If not, you can put your hand on the coil/coils and wires when the engine is running and see if you feel any small voltage leaking form the tune up parts.
It will leak secondary ignition voltage from the tune up parts caused by high resistance from carbon tracking if they are bad. This is very common if the tune up parts are not changed regularly!
If any is found, the tune up parts are simply bad and will need to be replaced! If none is found than you can spray a mist of water on the tune up parts when the engine is running and see if that causes the engine to stumble or run rough at all. Again, if it does, the tune up parts are bad and will need to be replaced!