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Integration help

  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

    Meir Achuz

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    Your integrand is of the form x/(ax+b).
    Write it as (1/a)[(ax+b)/(ax+b)-b/(ax+b)].
     
  4. Jun 5, 2007 #3
    1/30((142000+30v)/(142000+30v)-142000/(142000+30v))

    like this?

    what does this achieve?
     
  5. Jun 5, 2007 #4

    malawi_glenn

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    Well integrating functions of the type:

    x/(b-x) is pretty hard if you dont rewrite them..

    You will after a rewriting get things that has ln(x)-functions as primitive functions.

    Have you taken courses in calculus?
     
  6. Jun 5, 2007 #5
    nah im only in grade 12 in australia... i just need som help integrating this so i can solve a "flight" plan of a particle with variable acceleration... if you can help me with this it would be great
     
  7. Jun 5, 2007 #6
    if this is true:

    1/30((142000+30v)/(142000+30v)-142000/(142000+30v))

    how do i then integrate it?
     
  8. Jun 5, 2007 #7

    Meir Achuz

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    If you can't integrate that, take a day off and read a calculus text before continuing physics.
     
  9. Jun 5, 2007 #8
    im only in grade 12.... i dont have the time to take a day off or read calulus texts... i just need some one to tel me what to do and how to integrate it
     
  10. Jun 5, 2007 #9

    Meir Achuz

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    Can you divide (142000+30v) by (142000+30v)?
     
  11. Jun 5, 2007 #10

    Gza

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    Why do you insist on sticking those ugly numbers in, at every opportunity? Try working with the constants/variables you defined; much easier to solve problems this way (and makes troubleshooting a breeze.)
     
  12. Jun 6, 2007 #11
    yer you get

    (1/30)[(1/-142000)/(142000+30v)]

    now what?
     
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