So negatives always get me, no matter what and I'm having a hard time understanding the conservation of energy. Anywho, I'll continue. In a system, oh let's say a block on a rough surface with some intitial v and kinetic energy K at point A. After it gets to B, friction has done W amount of work on the block and now it has velocity ϑ and kinetic energy k. Consequently, K=k+W, so work by friction would be W=K-k, but then that means, algebraically, W is positive if the block is moving to the right. Friction always works against an object's velocity so the work is actually -W. Why doesn't the algebra show this? What am I missing?