No. Whiplash is caused by sudden forward acceleration. Your body accelerates, but your head doesn't, your neck muscles can't absorb the strain and your neck vertebrae don't bend that way. Acceleration in the other direction is less troublesome because your neck is designed to bend in the direction that your head moves in that circumstance, the motion being stopped when your chin hits your chest. Maybe you'll break your jaw, but your neck will remain undamaged. And, if your brakes are on, your car will be going slower when it hits the [hypothetical] car in front of you, thus reducing the impact.

But that's all irrelevant in any case. The original question was is it better to use the brakes or not. I'll try to make it really simple here.

The more brakes you have on at the time of impact, the less the car will move. The less the car moves, the less you move. The less you move, the less damage you will sustain.

It's A, B, C. Simple (very simple) Newtonian physics.

tanstaafl.