Final answer:
The elevator's acceleration is 1.5 m/s².
Step-by-step explanation:
The elevator's acceleration can be calculated by using Newton's second law of motion, which states that F = ma, where F is the force, m is the mass, and a is the acceleration.
In this case, the elevator's weight is equal to the force exerted by the elevator cable, which is 13,800 N. Therefore, the net force acting on the elevator is F = 13,800 N - 12,000 N = 1,800 N.
Using the formula F = ma, we can rearrange it to find the acceleration: a = F/m = 1,800 N / 1200 kg = 1.5 m/s².