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Minimum time interval problem

  1. Feb 28, 2008 #1
    1. The problem statement, all variables and given/known data
    A plane lands with a speed of 80.0 m/s and can accelerate with a maximum magnitude of 6.00 m/s^2 as it comes to rest. From the instant the plane touches the runway, what is the minimum time interval needed before it can come to rest?

    b. what is the minimum distance the plane requires to land?

    2. Relevant equations
    vxf-vxi=integral o to t axdt
    vxf=vxi+axt
    d=(vi+vf/2)t


    3. The attempt at a solution

    a. vi=80.0m/s
    vf=0m/s
    a=6.00 m/s^2

    Is this right so far?

    Would I then use the formula vxf=vxi+axt and solve for t?

    b. d=(vi+vf/2)t

    Now I just need to solve for d, right?

    Thank you very much
     
  2. jcsd
  3. Feb 28, 2008 #2

    berkeman

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    Staff: Mentor

    Looks right so far.
     
  4. Feb 28, 2008 #3
    Thank you very much

    Does this look correct?

    vi=80m/s
    vf=0m/s
    a=6.0m/s^2

    vxf=vxi+axt

    0m/s=80m/s+6m/s^2t
    t=-13.333

    d=vi+vf/2(t)
    d=(80m/s+0m/s/2)(-13.333)
    =-533.32

    but this can't be correct because the time and distance are negative.

    Do you see where I made my mistake?

    Thank you very much
     
  5. Feb 29, 2008 #4

    berkeman

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    Staff: Mentor

    You wrote: 0m/s=80m/s+6m/s^2t

    But the "acceleration" in this case is a deceleration, so the sign on the "acceleration" term should be negative.
     
  6. Feb 29, 2008 #5
    Thank you very much

    Regards
     
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