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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?

Thx in advance