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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- Aug 27th 2009, 04:07 AMcawcutt92displacement - 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? - Aug 27th 2009, 07:03 AMskeeter
$\displaystyle

x = 100(9.8t + 100 e^{-0.01t})

$

$\displaystyle

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

$

$\displaystyle

t = -100\ln\left(\frac{980-v}{100}\right)

$

sub in for t in x ...

$\displaystyle

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

$