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?
$\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]
$