# Thread: apinix's Request

1. ## apinix's Request

$\ddot {x} = \frac {dv}{dt} = \frac {P-mkv}{m} \\ \\ \therefore \frac {m dv}{P - mkv} = dt \Rightarrow \int \frac {mdv}{P - mkv} = \int dt \Rightarrow t = -\frac {1}{k} \ln (P - mkv) + C \\ \\ \therefore t_1 = -\frac {1}{k} \ln (P - 2mk) + C and t_2 = - \frac {1}{k}(P - 4mk) + C \\ \\ t_2 - t_1 = -\frac {1}{k} (\ln (P - 4km) - \ln (P - 2km)) = 5 \\ \\ \therefore - \frac {1}{k} \ln \left(\frac {P - 4km}{P - 2km} \right ) = 5 \Rightarrow \ln\left(\frac {P - 2km}{P - 4km}\right) = 5k \Rightarrow \frac {P - 2km}{P - 4km} = e^{5k}$

Rearranging you'll get: $P = \frac {2km (2e^{5k} - 1)}{e^{5k} - 1}$

I'm sorry I cannot type out the rest - I have a crook shoulder
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2. ## Re: apinix's Request

try \dot{x} and \ddot{x}
$\dot{x}\; \&\; \ddot{x}$

3. ## Re: apinix's Request

Originally Posted by dan964
try \dot{x} and \ddot{x}
$\dot{x}\; \&\; \ddot{x}$
Great. Thanks Dan.

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