Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

what is solution to mv' = -9.8m + kv with respect to t ? v(0)=v(0)?

a. v(t) = 9.8m/k + (v(0)+9.8m/k)e^(kt/m)

b. a. v(t) = 9.8m/k + (v(0) - 9.8m/k)e^(kt/m)

c. Neither

d.DNE

4 Answers

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  • Anonymous
    1 decade ago
    Favorite Answer

    mv' - kv = - 9,8

    This is a non homogen differential equation

    You have to solve first the homogen differential equation:

    mv' - kv = 0

    mv' = kv

    m dv/dt = k v

    m dv/v = k/dt

    int m dv/v = int k/dt

    m ln v = kt

    ln v = kt/m + C

    v = e^kt/m + e^C = A e^kt/m

    Now you have to calculate a particular solution from the non homogen differential equation and add both solutions.

    mv' = - 9,8 + kv accepts v = B,

    B a constant, as a particular solution

    0 = - 9.8 + k. B

    So, B = 9.8/k

    Now add both solutions:

    v = A e^kt/m + 9.8/k

    And use the initial conditions: v(0) = v(0) to evaluate A

    v(0) = A e^0 + 9.8/k

    So, A = v(0) - 9.8/k

    The solution is b. You mistyped it too.

    Ana

  • 1) Rewrite in terms of dv/dt.

    m(dv/dt) = -9.8m + kv

    2) Rearrange so v and dv are on the same side. This is a separable differential equation.

    [1/(kv - 9.8m)]dv = [1/m]dt

    3) Integrate both sides

    [ln(kv - 9.8m)]/k = (t/m) + C

    4) ln(kv - 9.8m) = (tk/m) + C

    5) kv - 9.8m = e^ [(tk/m) + C]

    6) kv = Ce^ [tk/m] + 9.8m

    7) v = [Ce^ [tk/m] + 9.8m]/k

    I don't think this matches A or B, so C.

  • 1 decade ago

    v'=dv/dt

    m(dv/dt)=-9.8m+kv

    m(dv)=-9.8m(dt)+kv(dt)

    take S as the symbol of integra

    S m(dv)=S -9.8m(dt)+S kv(dt)

    vm=-9.8mt+kvt

    v(m-kt)=-9.8mt=>

    v is a function of t=> v(t)=(-9.8mt)/(m-kt)

    I think the answer is "neither"

  • Anonymous
    1 decade ago

    Please put this in standard notaion....NO one, including myself, knows what the HECK you are talking about..

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