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Math Help - displacement - velocity equation

  1. #1
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    displacement - velocity equation

    i have the displacement equation:

    x(t) = 100[ 9.8t + 100 e^(-0.01t)]

    i need to get a displacement function with respect to velocity rather than time

    can anyone help?
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  2. #2
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    Quote Originally Posted by cawcutt92 View Post
    i have the displacement equation:

    x(t) = 100[ 9.8t + 100 e^(-0.01t)]

    i need to get a displacement function with respect to velocity rather than time

    can anyone help?
     <br />
x = 100(9.8t + 100 e^{-0.01t})<br />

     <br />
v = \frac{dx}{dt} = 100(9.8 - e^{-0.01t})<br />

     <br />
t = -100\ln\left(\frac{980-v}{100}\right)<br />

    sub in for t in x ...

     <br />
x = 100\left[-980\ln\left(\frac{980-v}{100}\right) + \left(\frac{980-v}{100}\right)\right]<br />
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