So recently a friend and I were pondering how much energy would be required to get a 20,000kg spaceship to 99% the speed of light. This arose from us discussing the raw efficiency of antimatter and how much antimatter would be required to fuel a spaceship to 99% C or 296794533.42 m/s. At first this seem simple since we thought we could use KE = 1/2mv^2 but then we realized we would have to take the change in relativistic mass into account. If I am not mistaken this is a differential equation as the ship's mass at any given point would be a function of its velocity. I am not experienced with problems of this sort. If anyone is willing to work out this problem for the hell of it I would much appreciate it. Also please tell me if I am overlooking something.