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First order ODE quesiton

  1. Oct 1, 2013 #1
    A particle of mass m is subject to a force F(v) = bv^2. The initial position is zero, and the initial speed is vi find x(t)

    so far

    m*dv/dx*v = -bv^2
    m*dv/dx = -bv
    integral m/-bv*dv = integral dx
    m/-b*ln(v) + a = x + b

    What do I do with the constants? i thought i was suppose to put in 'a' as vi and b as 0, but then when i integrate again for v, so i can get x(t) function, what do i use to fill in that constant?
     
  2. jcsd
  3. Oct 1, 2013 #2

    UltrafastPED

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    Where does m*dv/dx*v = -bv^2 come from? Newton's second law of motion implies F=m*dv/dt.
     
  4. Oct 1, 2013 #3
    dv/dx*v=dv/dx*dx/dt = dv/dt = a
     
  5. Oct 1, 2013 #4

    UltrafastPED

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    OK. You use your constants in the integrations: the lower constant on the dx integral is the starting location = 0, and the lower constant on the dv integral is the initial velocity = v_i.

    The upper constants are the unknowns ... your integral equation will provide a relation between them.
     
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