Newtons first law states that an object in motion stays in motion, and an object at rest stays at rest unless acted upon by a net force. So if you are driving at 100 miles per hour and hit a car, coming to a quick stop, your body will still want to continue at 100 miles per hour. Why doesn't it? Because the net force, your seat belt, is holding you back. Airbags also help to keep you out of danger. When cars were first designed, they had to think about the physics. The windshield would also stop you from going 100 miles per hour but that would be much more painful and it may not even stop you.
Overall, no matter how fast the car is moving, that's how fast we will be moving. I looked up when seat belts first became required and it wasn't til the late 70's til they were required for all passengers. 1686 was when Newton presented his three laws of motion in the "Principia Mathematica Philosophiae Naturali's." Weird that they were so far apart from each other.