1. 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?

2. Originally Posted by cawcutt92
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?
$
x = 100(9.8t + 100 e^{-0.01t})
$

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

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

sub in for t in x ...

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