I attached the problem and the solution. The book uses V has potential energy and T as KE. I'm not quite sure how they did this problem. I was following it until the 2nd to last line of equations. where they have "8.829-11.772+1/2*6*v^2+0=0" Why don't they have the KE for the 4kg carriage? It looks like they said that was 0, but isn't that still moving too?