I read in a book that if a lift descends with an acceleration of more than 9.8 metre per sec squared , the person would strike his head on the ceiling of the lift . I did the calculations and yes the reaction force is negative (in the same direction as weight) . But I don't quite understand how that works. I mean can't our body go down too? Not feeling very intuitive with this :/
Reaction force arises when the earth tries to accelerate the person with $g$ but the elevator stops the person by exerting the reaction force. When the elevator itself is falling faster than $g$, it cannot prevent the person from falling with $g$ and so reaction force is non existent. Since, the person is accelerating slower than the elevator, he goes upwards with respect to the elevator. And when he strikes the top, he is again prevented by the elevator from going any further by giving a reaction force in the downward direction.
If a lift suddenly began accelerating downwards (i.e. with an infinite jerk) at the same rate as $g$ then the person and the lift would fall together and the person would not hit their head on the ceiling of the elevator. They would feel weightless, but their feet would remain in contact with the floor until they pushed off from it. The elevator would have to accelerate faster than $g$ for the person to strike their head.