Accelerate very slow and rough

Hi I have a 1996 buick park ave from stop it accelerate very slow if i ease into the gas slightly it will speed up but very slow. If i press the gas harder it spits sputters and backfires it’s hard for me to accelerate fast with this problem making it unsafe for my family. I did replace the fuel pump a few months back . Any ideas for my vehicle problem? Plz and thanks

Is the Check Engine light on?

Tester

There’s so many things that could cause that symptom I doubt guessing will do much good for you. The advice above is good. Beyond that, first priority is to narrow the problem down to either spark, fuel/air mixture, exhaust, or major engine mechanicals. Where to start? That’s where a good shop will help. After you demonstrate it to them, they’ll likely have a good guess. If you don’t want to go that route, do it in the order above. Start by checking for a good healthy spark at all the spark plugs during cranking.

Classic fuel pump / fuel filter problem. Did you replace the filter when you did the pump?

To me this would, seeing as how the pump was changed, make me suspicious of the valvetrain and whatever system (belt, chain, variable valve timing?) controls the valve timing.

This happened on my 1991 Buick Park Ave that I had for a long time remembering it from the same thing on my other vehicle: If you have old plug wires, one or more is leaking through the broken down wire covering and grounding itself. This is easy to check out but in a very dark place. "SAFETY IS FIRST AS NOT TO PUT YOURSELF IN ANY POSITION THAT ANY PART OF YOUR BODY WILL BECOME A ITEM THAT THE CAR HAS A PATH TO YOU IF THE UNEXPECTED HAPPENS.
This first one should have no unusual danger that I can construe. Have the hood open. Have the parking brake on.
Have someone start the car and apply the brakes: If it is a leaking wire, you’ll see a white electrical arch jumping anywhere from the spark plug to the other end that goes to its’ end point. The front bank of plugs is easy to see but the back bank are against the fire wall. If nothing is seen, have the person that is inside the car increase the engine speed to about 1500 rpm, checking again.
If nothing, then a load needs to be in place and the SAFETY PART IS HIGHER: BODY& LIMBS are not a target of any part of the car. Person in the car has firmly applied the parking brake, the brakes are being firmly pressed; the car is put into gear and the rpm is brought up “some”, gradually. I500 RPM should be enough.
It only takes one arching spot to cause this problem.
When this happened to my Buick, the 2 above procedures did not create a visible arching. I surmised that I could not create the same hard load when the car was still from the actual conditions when acceleration was firmly made on the road. I replaced the plugs wires on a hunch and it fixed it.

Sounds like the engine is misfiring, consider replacing the spark plugs and ignition wires.