# displacement - velocity equation

• August 27th 2009, 04:07 AM
cawcutt92
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?
• August 27th 2009, 07:03 AM
skeeter
Quote:

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]
$