I am trying to solve a problem but I keep getting the wrong signs. Here is the problem:
While standing in an elevator, you see a screw fall from the ceiling. The ceiling is 3m above the floor. How long does it take for the screw to hit the floor if the elevator is moving upward and gaining speed at a constant rate of $a_f=4m/s^2$?
My idea was to combine the two accelerations of gravity and the elevator to get an equivalent acceleration of 13.8 for the screw. Then taking the upward direction as positive, we have that the screw displacement when it hits the floor will be -3, its final velocity will be 0, and its acceleration is -13.8. Thus using s=vt-0.5*at^2 we get -3=-0.5(-13.8)t^2 or -3=0.5*13.8t^2.
Why did I get a wrong equation? It appears that the minus should be a plus and this gives the right answer. However, I am not seeing where I got the signs wrong. If upward is +ve then the downward acceleration is -13.8 and the downward displacement is -3.