1. The problem statement, all variables and given/known data The problem regards a ball thrown vertically, there is a model of the motion that we worked out, from the original equation a(t) = -(g/b^2)(v^2+b^2) With some help from another forum member I integrated with regard to t (dv/dt?) this to t=-(b/g)(arctan(v/b)-arctan(v_0/b)) Where v is velocity, v_0 is initial velocity and b and g are constants The question then states - By writing a = v dv/dx, solve the resulting differential equation 2. Relevant equations I think this is somehow related to the chain rule as v dv/dx is equal to (dv/dt)(dt/dx) 3. The attempt at a solution The first integration is velocity with respect to time. I know that v dv/dx is a standard result found with the chain rule, in this case (dv/dt)(dt/dx). The problem I am having is where x comes into this, there is no mention of distance in any of the formulae I am using. How do I apply this to the problem?