A car moving at constant speed is suddenly braked. The occupants, all wearing seat belts, are thrown forward. The instant the car stops, however, the occupants are all jerked backward. Why? Is it possible to stop an automobile without this “jerk”?

Newton’s first law states that, without any external force, if a body is at rest, it will remain at rest and if the body is moving with constant velocity, it will continue to do so. When the car is suddenly braked, due to the inertia, the occupants in the car will tend to move in the forward direction of car. When the car stops the sit belt in the car will produce backward momentum on the occupants. Since the all the occupants wearing seat belts, therefore the occupants are all jerked backward.
Yes, it is possible to stop an automobile without this jerk. This can be done by slowing down the car a little longer time.