Do your brakes, in addition to stopping the wheel rotation, also drive pylons into the ground to keep your wheels planted at the exact spot they stopped on?

If you keep your brakes on, the acceleration at the beginning and end of the car's movement will increase significantly, as the wheels overcome and then get overcome by the static friction of the rubber on the road. If your wheels can rotate, as soon as the impacting car touches you, your car will start accelerating, and assuming that you don't slam on the brakes after impact, the stopping acceleration will be no more than what you normally experience.

Actually, that's a good analog. You currently have the ability to stop your car fairly fast or fairly slowly. Do you stop your car as quickly as you can? If not, why not? Is it because it puts more strain on your body?