might have misaligned or loose wheels
Warped rotor and worn out brake pads.
Wheels require balancing.
The pistons are running in the cylinders of the engine, so when the rpm of the engine rises, the pistons quickley build up speed. It is this rapid acceleration of the pistons that casue the car to shake.
If a car shakes during acceleration the brake rotors may be damaged. If the rotors are damaged they will be unstable as the tires rotates making the whole car shake.
the cuase of this is ussaully worped rotars
only when it is on, it causes slow acceleration
Thankfully mine does not shake, thanks for asking. This is really not enough information to diagnose the problem. Does it shake the same every time or does it not shake or shake less sometimes? Is the "check engine" light on? Is there a speed where the shake is more pronounced? Does it have to be full throttle acceleration or does it shake under light acceleration too? Is there a noise accompanying the shake? If you accelerate around a corner is the shake any different? Left or right turn make a difference?
Could be a problem with your torque converter
only if it is loud, and it mostly causes slow acceleration
Try changing the ignition wires
Cylinder miss, broken motor mount, or vacuum leak.
Mabey you are low on gas or mabey a ring of som sort for ex: Piston ring