The approach to this problem uses Newton's Laws and the main step is summing all the forces in the system. Since forces are only in the vertical direction and that the elevator is in motion then it follows:
Sum of Forces (y axis) = Force of Tension + Force due to Gravity = ma (because we are in motion)
Force of Tension is +3500N (choosing up as positive)
Force due to Gravity = 450kg * (9.8m/s) = 4410N
+3500N  4410N = ma = 450 * a => solving for a = 910N / 450kg = 2.02m/s^2
So the elevator is moving downward at 2.02 m/s^2
10/16/2013

Alex V.