Mine did the same thing. It would get better when I got up to 50+. Turned out to be the CV joint. Replaced the whole axle for around $80(part only).
One of the possible causes of a Pontiac Bonneville to jerk during acceleration is that the car needs a tune up. The engine misfiring can lead it to jerk as you accelerate.
During acceleration? I'm not sure. But when both idling and acceleration the engine's combustion can cause a lot of vibration in the steering wheel if you are in an older vehicle.
Fuel Pump
Bucking during acceleration can be caused by a low fuel level. When the car is running on fumes, it is not getting a constant supply of gas which will cause it to stop and go.
try changing plugs and wires
There are numerous issues that can cause a lack of power during acceleration. Common causes include a clogged fuel filter, a clogged air filter, and dirty fuel injectors.
A bad o2 sensor can cause this problem in a car. A bad fuel pump, fuel filter or fuel line will also cause hesitation during acceleration.
Driving at 50mph or above what causes a loud knocking clicking sound during acceleration?
Bad tire? Bad wheel bearing? Bent wheel? Bent axle?
Try doing a tune up. Change sparplugs,wires etc.
Try disconnection your MAF ( mass airflow sensor ) and if it doesn't sputter when you accelarate, it means your sensor is gonzo.
The vibration at speed is more than likely a tire out of balance or a tire with a broken belt. Have this checked ASAP. The pulsation during acceleration can be many things, from a vacuum leak to a clogged fuel filter. Take it to a tech for service.