1. The problem statement, all variables and given/known data If the acceleration of a particle is given by a=k*x*v , where x is position, v is velocity and k is constant and positive, and in t=0: x(t=0)=0 and v(t=0)=vo; find x(t) and x(v). 3. The attempt at a solution I arrived to dx/dt= k/2*(x2-xo)+vo , (xo=x(t=0)=0). Then I tried to solve the (definite) integral (from 0 to x) ∫1/((k/2)*(x2)+vo)dx that is equal to ∫dt = t. In this integral (which I just couldn't solve) I took vo as a constant. My idea was to solve (result of the integral)=t for x(t). Is this the right way to do it? If so, how can I solve the integral? Thanks!