Car: 98' Pontiac Grand Prix

Issue: Whenever I'm driving and I start to accelerate my car begins to "pull forward" forcefully.

Example: I'm ready to get on the highway; I begin to accelerate till it reaches 60 mph, throughout this process the car vibrates and begins to pull itself forward, like if it is forcing itself to reach to 60 and than I let go of the gas and it stops.

Why is this happening?

Where do you feel the vibration is coming from? Is it in the front end or can you feel it in the steering wheel? Or does it seem like it's coming from the motor?

Does this only happen until you reach 60mph or is it every time you accelerate?

Where do you feel the vibration is coming from? Is it in the front end or can you feel it in the steering wheel? Or does it seem like it's coming from the motor?

Does this only happen until you reach 60mph or is it every time you accelerate?

It feels like in the middle bottom of the car. And it happens whenever I try to reach 40 or above.

I'd have your front end parts checked, as well as your wheel bearings.

I'm not sure I get the exact picture. Have you replaced the platinum spark plugs (ACDelco only) in the last 50,000 miles? Could the old plugs be breaking down under load?

My experience with this kind of accel vibration has always turned out to be worn CV drive axles. Mostly the inner CV joints.
I could be way off, but something don't sound right in the front end department.