(A) The final velocity is
[tex]12\ m/s\ up+4\ m/s^{2}\ down*3\ s[/tex]
[tex]=12\ m/s-4\ m/s^{2}*3\ s[/tex]
[tex]=12\ m/s-12\ m/s[/tex]
[tex]=0[/tex]
So the elevator has final velocity 0 (and no direction).
(B) The distance moved is
[tex]d=v_{i}t+\frac{1}{2}at^{2}[/tex]
where [tex]v_{i}=[/tex] the initial velocity, [tex]a=[/tex] acceleration, and [tex]t=[/tex] time.
So we get
[tex]d=12\ m/s*3\ s-\frac{1}{2}(4\ m/s^{2})(3\ s)^{2}[/tex]
[tex]=36-2*9[/tex]
[tex]=36-18[/tex]
[tex]=18\ m[/tex]
so the elevator moved 18 meters upwards.
