# Integration trouble

#### tomwilliam

I'm just playing around with a linear air resistance model to show that a marble, diameter 2cm, mass 13g, takes 3.96 seconds to fall 77m off a bridge to the water. I've done it by starting with

ma = mg - c1Dv

Where m is mass, D is diameter, v is velocity downwards and a is acceleration (g).
Now I can divide by m, then integrate twice with respect to t, and solve the quadratic equation to get the right answer. However, that involves a square root calculation. I'm preparing for an exam in which I won't have a calculator, so it might be best to do it a different way.
The book tells me to divide by mg - c1Dv, then integrate wrt t, giving
-1/k ln (g - kv) = t + A

Where k= c1D/m. Here's the problem...I'm not really sure how we got that result, nor where to go from here. Any helpful hints?

#### tomwilliam

Not that it matters, but I have the value for c1, which I forgot to mention (1.7 x 10^-4)

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