Question

A certain elevator cab has a total run of 193 m and a maximum speed is 322 m/min, and it accelerates from rest and then back to rest at 1.18 m/s². (a) How far does the cab move while accelerating to full speed from rest? (b) How long does it take to make the nonstop 193 m run, starting and ending at rest?

Answer 1

Given Data:

The total distance is,

The final speed is,

The acceleration is,

Part (a):

For the acceleration process, the distance from the rest is given as,

Here, x₀  is the initial position (0 m), and x₁is the final position.

Substitute the values in equation (1)

Part (b):

The total time due to the acceleration process is given as,

For the acceleration process, use the first equation of motion,

For the deceleration process, use the first equation of motion,

Substitute the values in equation (2)

The total distance with respect to the acceleration is,

Hence, the time interval for displacement due to non-stop run with the constant velocity is,

The total time for the whole process is,