Hello PF,(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Deriving terminal velocity

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