There are several reasons why a car may shake at low speeds, such as bad motor mounts, warped rotors and unbalanced wheels. To narrow down the problem the braking components, wheels and mounts of the vehicle should be inspected.
A common cause of a low speed vibration is a warped rotor. The rotors of a vehicle are found on each wheel assembly. A caliper compresses on a rotor assembly to stop the vehicle. When a rotor warps the wheel spins at an angle as opposed to straight. This causes the brake pads to wear unevenly and the car to shake when stopping.
An unbalanced wheel is more noticeable in higher speed ranges. It usually becomes a problem when traveling between 50 and 60 mph. The angle at which the wheel is spinning will be felt by the cabin of the vehicle. In more serious cases the vibrations from the unbalanced wheel is felt while accelerating.
If the problem is centralized inside the engine bay then it may be one of the motor mounts. A worn motor mount will cause the violent vibrations of the engine to be felt inside the cabin of the vehicle. To inspect an engine mount, open the hood and look at the mounting bolts or rubber inserts. If the inserts are worn or cracked the mounts will need to be replaced. If the bolts are off center the mounts will need to be properly adjusted.