Several things causes a car to shake.
Cars can shake as a result of issues with loose wheels, unbalanced tires, damaged tires, worn motor mounts, misfiring engine, problems with the brakes, warped brake rotors or loose or worn ball joints and other suspension problems.
If the vehicle has a drive shaft and is rear wheel drive bad U Joints can cause the vehicle to shake as you accelerate.
If your car or vehicle is front wheel drive then bad CV joints could also cause your car to shake as you accelerate.
If the shaking of the car occurs when braking, it often indicates a problem with the brakes, like warped rotors, worn brake pads or even a stuck brake caliper.
If the car shakes during accelerating, it can be an issue with engine misfire, bent axle, worn CV joints, loose CV joints etc.
If the shaking of the car occurs between 20 mph to 30 mph but the shaking stops at higher speeds it could be a result of bad or unbalanced tires.
If the car shakes while idling it can signal that you have engine trouble, like a misfiring engine cylinder which could be due to bad spark plugs, bad spark plug wires, bad ignition coils, etc.
Or the shaking could also be a problem with the motor mounts.
Common causes of a car shaking are unbalanced tires, uneven tire wear, out of round tires or even loose lug nuts and even bad spark plugs, bad ignition coils, low fuel pressure, bad fuel pump or clogged fuel filter, and in some cases a dirty air filter.
Warped brake rotors are also a common and frequent cause of cars and vehicles shaking, especially when braking.
And worn out or loose suspension parts such as tie rod ends, ball joints or damaged axles or even bent driveshaft, worn CV joints or U Joints can also cause cars and vehicles to shake when power is transferred to the wheels upon acceleration.