(1 point) For this problem y is the variable for the displacement, V is the velocity, m is the mass, k is the constant of proportionality. The force on the object is the mass times the acceleration: F : | (in terms of y) In terms of the velocity v we have F = For an object in free fall there are two forces: the force due to gravity (positive 9) and the force due to air resistance, which is proportional to the velocity and acts in the opposite direction. Therefore F 2 Putting these two together we get a differential equation for the force acting on an object in free fall in terms of the velocity v: : 0. This equation is separable: v' : 1, so we can integrate both sides with respect to t. If we integrate both sides, combine all constants into one constant v0 then we get 12 : . Integrating again we find that y : , where we use yO as the integration constant