To brake or not to brake? Is there a question?

The vehicle following problem in an automated highway is approached from the point of view of safety. In particular the situation where an intervehicle collision is unavoidable and the relative velocity at impact is what determines the safety of the situation, is considered. It is shown, using tools from optimal control, that braking as hard as possible is not the best possible strategy in all cases. More importantly, the assumption that the worst that the vehicle ahead can do is to brake as hard as possible may also be incorrect.