Hello PF, I have once simple (well, not so simple for me) question. I'm trying to derive an equation for the velocity of a falling body with accordance to terminal velocity. The equation incorporates drag proportional to the speed. m*dv/dt=mg-bv and mg/b=terminal velocity v_{t} So the steps I took were: m*dv/dt+bv=mg (m/b)*(dv/dt)+v=v_{t} dv/dt=(b/m)(v_{t}-v) dv/(v_{t}-v)=(b/m)dt Integrating both sides would give ln[(v_{t}-v)/(v_{t)}]=(b/m)t But the textbook says that I'm supposed to get negative (b/m)t on the left side. Have I made a mistake on the integration part? Any help will be deeply appreciated.
hmm. I seem to have gotten the answer if I just divided the entire equation by -b in the beginning without bringing the bv to the left side. Have I made a mistake on the integration part?