Some of the answers are implying that the answer lies within the quantum effects of the electron, but there's a pretty intuitive answer if you think of the system as classical -- and I suspect the quantum answer is just a slight modification of this. 

If you could pull the nucleus of an atom on a string, there will be some speed where if you tug it too hard the electron will get left behind. 

Comparing to your example: A car suddenly stopping will cause a person to fly into the windshield. But a car that doesn't stop as sudden will not cause a person to have any issues. This is because the friction between the person and the car keeps them in equilibirum dispite the additional inertial force.

Another example: If the was sun moved slowly enough, the planets would still follow it in orbit. But if the sun was jerked away too quickly, many or all of the planets could get left behind.