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Math Help - Modelling using differential equations

  1. #1
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    Modelling using differential equations

    A particle of mass m is released from rest at time t = 0 at some height above the ground. It experiences a resistance mkv where v is its speed and k a constant. Find v and the vertical distance fallen after time t.

    I admit I am a little lost on this question, so any help would be appreciated.
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  2. #2
    Super Member Showcase_22's Avatar
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    I think it goes a little like this:

    F=ma

    F=m\frac{dv}{dt}

    mg-mkv=m\frac{dv}{dt}

    g-kv=\frac{dv}{dt}

    Then it's separation of variables or integrating factor to get an equation for v in terms of t.
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  3. #3
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    Quote Originally Posted by Showcase_22 View Post
    I think it goes a little like this:

    F=ma

    F=m\frac{dv}{dt}

    mg-mkv=m\frac{dv}{dt}

    g-kv=\frac{dv}{dt}

    Then it's separation of variables or integrating factor to get an equation for v in terms of t.
    And once v = v(t) is got, it's not hard to get x = x(t) from it.
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