Originally Posted by

**acevipa** Thanks that makes a lot of sense.

$\displaystyle a=-kv^2 \Longrightarrow \dfrac{dv}{dt}=-kv^2$

$\displaystyle v\dfrac{dv}{dx}=-kv^2$

$\displaystyle \dfrac{dv}{dx}=-kv$

$\displaystyle \displaystyle\int\dfrac{dv}{v}=\int -k \ dx$

$\displaystyle \ln v=-kx+C$

When $\displaystyle x=0, v=20 \Longrightarrow C = \ln 20$

$\displaystyle \ln v =-kx+\ln 20$

When $\displaystyle x=100, v=10$

$\displaystyle \ln 10=-100k+\ln 20$

$\displaystyle 100k = \ln 20 - \ln 10$

$\displaystyle 100k = \ln 2$

$\displaystyle k = \dfrac{\ln 2}{100}$

Have I done everything right? If so, I'm not too sure what to do next.

The answer in the book is $\displaystyle 20\ln 2$