CAR JUMP WHEN I ACCELERATE UP TO 40 MPH - 1992 Mercury Grand Marquis

SOURCE: the car will not accelerate;

this sounds like 1 of 2 possible problems.
a bad headgasket or a clogged catalytic convertor. i would lean more towards the convertor

SOURCE: Car shudders when accelerating...

My wife's 02 Audi A4 1,8t had the same problem after talking with Audi (coil pack/spark plugs) we replaced them all and the problem still persisted not to say that won't fix your problem but what I found to be the problem was 3/8 vacuum line (shaped like a S) that comes up on the right hand side between the oil filter and the fire wall that comes from the turbo check valve assembly (its hard to locate and should be done with the engine cool) up to a valve assembly that connects to the intake manifold, what was happening was the hose would become spongy at the bottom (you will have to squeeze the hose from top to bottom to notice the difference) and as the engine heats up it would cause the hose to collapse. Once I replaced the hose and the computer reprogrammed the fuel mixture (about 25 miles of driving) the problem seems to have been correct. Good luck.I had also replaced the turbo check valve about three years ago because of a severe hesitation when you first apply gas (turbo check valve may not be the proper name.) Sorry. Wife Still Loves Her Audi

SOURCE: Hyundai Sonata 2002 idle at high RPM and accelerate 40-45 MPH

Look for a vacuum leak somewhere. This is the most common problem for a high idle.

SOURCE: 2000 HYUNDAI SONATA RADIO DOES NOT WORK AFTER BATTERY JUMP?

Does the Check Engine light come ON when this happens? Whenever the "Check Engine" light comes on, there is always a DTC (Diagnostic Trouble Code) stored in the ECM (Engine Control Module). You'll need an OBDII (On-Board-Diagnostics) scanner to retrieve any codes recorded/set in ECM. Once you do this and let us know what, if any codes are set, then we can go from there.

SOURCE: 2002 Alero wont go over 40 mph

I happen to own a 2002 alero, and my wife called me and said the same problem had happened. Change your fuel filter.