1. The problem statement, all variables and given/known data A body of unit mass, whose position is x(t) is subject to a velocity-dependent force of the form F=a(dx/dt)-b(dx/dt)^2 where a and b are positive constants and the positive x direction is to the right. a) Write down the equation of motion b) If the motion is initially to the right, what would be the velocity for t->infinity? 2. Relevant equations 3. The attempt at a solution Part a is straight forward. Since m is a unit mass, we can set m=1. Then we have F=(1)x''=ax'-b(x')^2 =>x''-ax'+b(x')^2=0. But I do not know how to start with part b. The solution says "the equation has fixed point at v=a/b so it will asymptotically reach a/b as t->infinity" but I am not sure how this came about. Why set x''=0 to find the velocity at t->infinity? Thanks!