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Math Help - can't prove acceleration,slight worry

  1. #1
    Member i_zz_y_ill's Avatar
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    can't prove acceleration,slight worry

    A rock falling under its on weight and resistance r=0.001mv^2

    show newtons second law gives vdv/dx=g-0.001v^2

    Am I missing something?? when did vdv/dx = a having cancelled through by m
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by i_zz_y_ill View Post
    A rock falling under its on weight and resistance r=0.001mv^2

    show newtons second law gives vdv/dx=g-0.001v^2

    Am I missing something?? when did vdv/dx = a having cancelled through by m
    You should know a = \frac{dv}{dt} = \frac{d^2 x}{dt^2} and v = \frac{dx}{dt}.

    Use the chain rule:

    {\color{red}a = \frac{dv}{dt} = \frac{dv}{dx} \cdot \frac{dx}{dt} = \frac{dv}{dx} \cdot v}.

    Using the chain rule again it follows that a = \frac{d}{dx} \left[\frac{v^2}{2} \right].
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