"A particle is relased from rest (y = 0)and falls under the influence of gravity and air resistance. Find the relationship between v and the distance of falling y when the air resistance is equal to a) av and b) Bv^2." I already solved part a by integrating dv/dt = -g - (a/m)(dy/dt) with respect to t to give me v = -gt - (ay/m), and then taking force = m(dv/dt) = -mg-av and rearranging this to give me dv/(g + av/m) = -dt, which I integrated to get (m/a)ln(av/m + g) = -t + c. Solving for c and doing some algebra gives me y = -(m/a)(v -(mg/a)ln(av/mg + 1)) as my final solution for y. Part b, though, I have no idea how to do. If I try and solve it the same way, I end up with the integral of dv/(g + av^2/m) with respect to time, which I have no idea how to solve. I also have the integral -g-(av^2)/m with respect to time, which I don't know how to solve either. If anyone can help me solve these integrals, or point out an easier way to solve this problem, I'd be most grateful.