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Acceleration proportional to velocity

  1. Aug 31, 2010 #1
    1. The problem statement, all variables and given/known data
    A particle is accelerated from rest with acc. proportional to velocity. After traveling 10 meters the speed is 35 m/s, find the speed after the particle traveled 20 meters. (Changed the numbers a bit from the original so the answer ppbly will not be clean.)

    2. Relevant equations

    a=v dv/dx possibly

    3. The attempt at a solution
    Sat on this one for a long, long time

    Tanks in advance
     
  2. jcsd
  3. Aug 31, 2010 #2

    HallsofIvy

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    "Tanks"?

    No, a is not "v dv/dx". Rather a= dv/dx which, here, is proportional to v:
    a= dv/dx= kv for some number k.

    From that dv/v= kdx. Now integrate both sides.
     
  4. Aug 31, 2010 #3

    diazona

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    a = dv/dt, I think you mean?
     
  5. Aug 31, 2010 #4
    Yea, watch out for those advancing tanks; hah, no I meant to say thanks.
    Anyway, I do believe that a= v dv/dx ; dv/dt = (dv/dx)(dx/dt) = v (dv/dx). Does this seem reasonable:
    a=kv=v dv/dx
    k=dv/dx
    k dx = dv
    intg.
    v=kx
    ??? or is dividing by v not allowed => loss of roots or something???
     
  6. Aug 31, 2010 #5

    diazona

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    I do believe you're right, a = v dv/dx. (In one dimension of course) And I don't see anything wrong with your work.

    Can you think of a reason why dividing by v would not be allowed? (hint: what number(s) are you not allowed to divide by?)
     
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