You should check the timing and plugs.
There could be many reasons, a vacuum leak is one possibility.
A miss or A collapsed engine mount or A imbalance caused by a failing component, harmonic balancers and torque converters are common.
You could have a spark plug wire going bad. When idling it has the lowest demand, and when put under a load, higher resistance causes it to hunt a ground with the least resistance which may not be through the spark plug, therefore causing a misfire.
This may be the indication of a spark plug miss.
A bad distributor cap, Plug wires, spark plugs,This is not common, but a bad injector could cause a miss too. I would do a tune-up first. If you don't find the problem in the tune-up area, then please ask your question again.
Engine miss.
could need a good tune up sounds like it has a miss
bad coil pack bad plugs bad wires water and water in your fuel system
I would suspect a vacuum leak. If the car is over 10 years old, I would recommend you replace all vacuum hoses under the hood. Do them one at a time as to not get confused.
A bad spark plug, spark plug wire, distributor cap, rotor, fuel injector or burned valve.
You May Have Broken A Plug Wire. Gently Remove Each Plug To See If You Haven`t Cracked One, Or Closed The Gap. If They Are OK. You Most Likely Need Wires. Hope This Helps. Replace the spark plug wires. You have one that is bad. Also look for a broken or disconnected vacuum line.
bad distributor cap would be first choice, next would be the rotor button in distributor.then the coil