Consider a system in which you have a rope connected to 1 pull above (A) which connects to a pull below (B) in which some object of mass 10kg is attached To the pully(not the rope). The rest of the rope goes to the celing which contains infinite rope.
I know that there is 2 tensions acting on this rope (the left side) and (the right side). So if I want to raise this object by say 1 meter how will I mathematically explain that I must pull down the rope with twice the distance. I cannot seem to prove this mathematically using the simple kinematic equations because if you pull with a force = to the weight of the object it rises with constant speed. i cannot find this speed and therefore cannot find the time so that I can calculate the position.