When I accelerate, the car shakes.
I believe what you are experiencing is a misfire condition. Basically, this is when one or more of the cylinders in your engine stop producing power due to a lack of fuel spark, or oxygen, that is necessary for combustion. Generally, your concern is related to the ignition system, or spark, of your engine. A qualified technician will be able to determine what is causing your engine to sputter with a thorough inspection of the source of the shaking, so you can get your car back on the road again. A YourMechanic technician can come to you to make these repairs.