The Elevator An express elevator is to carry passengers from ground level to a l

Question

The Elevator

An express elevator is to carry passengers from ground level to a lobby where they can catch elevators to higher floors. This express trip is 80m of vertical rise.

The constraints for the design are

1) that the acceleration cannot change by more than (+-)1.5 m/s^3; that is the jerk is limited to (+-)1.5 m/s^3; and

2), that the acceleration itself should never exceed (+-)1.5 m/s^2; and

3), that the velocity should never exceed (+-)5 m/s.

Find the least time that will take passengers from a stop on the ground floor to a stop at the lobby. Determine the piecewise function that describes velocity during an ascent.

Explanation / Answer

Simple and Correct:

time to reach the acceleration = 1 sec

distance covered = jt3/6 = 1.5/6 = 1/4 = .25 m

velocity = jt2/2 = 1.5/2 = .75m/s

time taken to reach 5 m/s = 2.833 more sec

distance = vt + at2/2 = .75x2.833 + 1.5x2.8332/2 = 8.144 m

distance remaining = 71.6 m

time taken to cover = 14.321 sec

total time = 18.154 sec

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