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Homework Help: Integration (displacement or position)

  1. Jun 4, 2007 #1
    1. The problem statement, all variables and given/known data
    the trouble is in the integration on the left side (go straight o my answer down the bottom of the page)... please help me...

    mg-u-kv=m*a

    where (all constant)
    m= mass= 3000
    g=gravity=10
    u=thrust=172000
    k=30

    v=velocity=variable
    a=acceleration=variable


    2. Relevant equations

    accel=v*dv/ds=dv/dt=a

    3. The attempt at a solution

    30000-172000-30v = 3000*v*dv/ds
    -142000-30v = 3000*v*dv/ds
    -(142000+30v) = 3000*v*dv/ds
    142000+30v = -3000*v*dv/ds
    (142000+30v)/v*dv = -3000*ds
    v/(142000+30v)*dv = -1/3000*ds

    and then integrate both sides, this is where my calculus stops

    i know the right side (-1/3000*ds) becomes -1/3000s + c
    where
    s= displacement or position and
    c= constant
    i have 2 scenarios

    when s=0, v=1000
    and what i need to find is when v=0 what is s?


    so once i integrate the left side i sub those values in.
     
  2. jcsd
  3. Jun 4, 2007 #2
    Are you sure about this transition?
     
  4. Jun 5, 2007 #3
    if you think you can do it without that transition... go for it... that's just how i interpreted the question
     
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