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Solving 2.52 Elevator Problem how to calculate time of a complete trip?

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi everyone, Im just wondering how you would solve this question..
    2. Elevator Problem (Practice on Segmented Motion)
    A hotel elevator ascends 200 m with maximum speed of 5 m/s. Its acceleration and
    deceleration both have a magnitude of 1.0 m/s
    How long does it take to make a complete trip from bottom to top.


    2. Relevant equations
    xf = xi + vi Δt + 1/2aΔt^2
    v = vi + a*t


    3. The attempt at a solution
    There was another part to this question which asked me to solve for how far the elevator will move while accelerating to full speed from rest, and I got 12.5 m for that.
    Do I plug in 12.5 m into this equation and solve for t? Thank you!
     
  2. jcsd
  3. Oct 14, 2012 #2

    cepheid

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    Staff Emeritus
    Science Advisor
    Gold Member

    Welcome to PF crystaldreams!

    Assuming you did the first part right (EDIT: and you did), then the elevator will accelerate upward for the first 12.5 m, cruise at the max speed for 175 m, and then accelerate downward (meaning decelerate: i.e. reduce its upward speed) for the final 12.5 m, bringing it to a rest at the top. All you have to do is calculate the time required for each of these three phases of motion using the kinematics equations.
     
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