1. The problem statement, all variables and given/known data A particle of mass m slides down an inclined plane under the influence of gravity. If the motion is resisted by a force f = kmv^2, show that the time required to move a distance d after starting from rest is t = [arccosh(e^(kd))]/√(kgsin(θ) where θ is the angle of inclination of the plane. 2. Relevant equations F = ma F_g = mgsin(θ) Resistance = -kmv^2 Motion of particle => ma = mgsin(θ) - kmv^2 3. The attempt at a solution My attempt was to set up the equation for the motion (ma = mgsin(θ) - kmv^2) and use differential equations to solve. After dividing by mass, I had: dv/dt = gsin(θ) - kv^2 which I then divided by k, and substituted (g/k)sinθ for C^2 giving dv/kdt = C^2 - v^2 After collecting terms and integrating I came to t = arctan(v/√((g/k)sinθ))/√(kgsinθ) I thought I was on the right track as I have the numerator correct, but I do not know where to go from here, or if this is even correct so far. Any help would be much appreciated. Also, I know this question has been asked before, but the answer given didn't make sense to me so it doesn't help.