Kinematics question - elevator problem

AI Thread Summary
To program an elevator's vertical motion from one floor to the next, it must cover a distance of 5.0 meters while adhering to speed, acceleration, and jerk constraints. The maximum speed is limited to 1.0 m/s, with acceleration capped at 0.50 m/s² and jerk at 0.50 m/s³. The optimal motion sequence involves gradually increasing speed to the maximum, maintaining it, and then decelerating smoothly to ensure passenger comfort. Calculating the time for the trip requires integrating these motion parameters, factoring in the constraints to determine the total duration. Understanding the relationships between speed, acceleration, and jerk is crucial for solving this kinematics problem effectively.
drg1233
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Kinematics question...?
you are asked to program a sequence of vertical motions for an elevator to take it from one floor in a building to the floor directly above, a total distance of 5.0m. In order to ensure that the ride is safe and comfortable for passengers, the elevator's motion is subject to the following constraints:

1. The speed can't be >1.0 m/s
2. The magnitude of the acceleration can't be > 0.50 m/s^2
3. The magnitude of the acceleration's rate of change ("jerk") can't be >.50m/s^3

a. What sequence of motions will get the elevator from one floor to the one directly above as fast as possible?
b. how much time does the elevator's trip take from one floor to the floor directly above?

I have some graphs of acceleration and velocity graphs, but i honestly don't really know where to start.
 
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Units of "jerk" or "surge" are m/s3.
 
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