Note that this is a first year, Calculus 12 DE question:
The velocity,v, of an object falling through the Earth's atmosphere obeys the DE dv/dt=g-kv, where k is the called the drag constant and g is the gravitational constant. This equation states that the acceleration of the object is g reduced by an amount that represents air resistance (kv). Air resistance is proportional to the velocity of the object.
a) Find the function v(t) assuming that v(0)=0.
All first year calculus methods used to find DE's.
The Attempt at a Solution
I just seem to be lost on how to convert the derivative given into an equation that contains the variables given by dv/dt. I have no problems finding antiderivatives, it just seems to be the introduction of variables instead of numbers here that is throwing me off. If anyone can point me along in the right direction it would be greatly appreciated, thanks in advance.