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## Homework Statement

Under some circumstances a falling body B of mass m encounters air resistance proportional to its instantanous velocity v. Use Newton's second law to find the differential equation for the velocity of v of the body at time t. Recall that acceleration a = dv/dt. Assume in this case that the positive direction is downward.

## Homework Equations

F = ma

a = dv/dt

air resistance = kv

kv = mg

## The Attempt at a Solution

kv = mg (dv/dt)

(dv/dt) (k/m) v = g

The solution in the text is (dv/dt) + (k/m) v = g.

I'm failing to understand why (dv/dt) is added to (k/m).