1. The problem statement, all variables and given/known data A vehicle of mass m experiences a constant frictional resistance ma and air resistance proportional to the square of its speed. It can exert a constant propelling force mb and attain a maximum speed V Show that, starting from rest, it can attain the speed V/2 in the time Vln3/2(b-a) And that the friction and air resistance alone can then bring it to rest in a further time (V/(a(b-a))^1/2)tan-1(b-a/4a)^1/2 2. The attempt at a solution Using mc as the constant of proportionality for air resistance yields: x''=b-a-c(x')^2 from there I'm just guessing as to the method but I've tried this: dx'/dt=b-a-c(x')^2 int(dx')=int((b-a-c(x')^2)dt) =(b-a)int(dt)-c(int((x')^2dt) =(b-a)int(dt)-c(int(x'dx)) but I'm not sure how to integrate x' w.r.t. x? Of course I could be going about it completely the wrong way. The motion is in one dimension so I could maybe import one of the equations of motion, like v^2=u^2+2as? I'm sure I'm missing a trick (or two) somewhere.