Q: Car vibrates when I accelerate at a low speed. Between 1000 & 2000 rpm

Shaking or vibration may be caused by many different things such as faulty spark plugs, poor fuel pressure or misfires. Other things such as a faulty idle air control valve may cause the engine idle to drop below the normal idling RPM which may also cause the motor to shake or vibrate more than normal. This creates a loss of power that resonates throughout the motor additionally causing other problems with ignition and fuel timing. Anytime a misfire is caused, this causes an imbalance in the motor which will cause the motor to shake or vibrate. Other issues that may cause this type of shaking or vibration might be broken engine mounts or potentially tires that are out of balance or worn improperly. Engine mounts are generally rubber mounted braces that hold the engine in place to the chassis of the car. When these break or become weak or faulty, this may cause the engine to vibrate heavily. When tires are out of balance, as the speed of the vehicle increases, the vibration will become much more noticeable and pronounced. I would suggest having an expert from YourMechanic come to your location to diagnose and inspect your vehicle using a scanning tool which will more accurately indicate what specifically may be causing this.