Final answer:
The shortest time for the elevator to reach a floor 12 m above the ground is determined by calculating the time for acceleration and deceleration separately. Utilizing the kinematic equations, the total time is found by adding the times for both phases, considering acceleration and deceleration rates.
Step-by-step explanation:
To determine the shortest time it takes for the elevator to reach a floor 12 m above the ground, we need to calculate the time taken for the acceleration and deceleration phases separately. First, we calculate the time taken for the elevator to accelerate to its final velocity before deceleration. Using the equation: vf = vi + at. where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time, the initial velocity vi is 0 m/s and the final velocity vf can be calculated using: vf^2 = vi^2 + 2ad. where d is the displacement. Rearranging the equation, we get vf = sqrt(2ad). Plugging in the values of a = 1.5 m/s² and d = 12 m, we can calculate vf and subsequently the time taken for acceleration. The time taken for deceleration can be calculated using the same equation but with the deceleration rate a = -0.6 m/s². Adding the times for acceleration and deceleration will give us the total time taken for the elevator to reach the desired floor.