It seems to tell us that it takes more and more energy to increase by the same amount of speed. I don't actually expend 3 times as much gas accelerating my car from 50 to 100 as I did going from 0 to 50: If e=1/2mv2, it tells us how much 'kinetic' energy exists within a moving object -say relative to us. In order to obey the Law of Conservation of Energy, the amount of kinetic energy that exists within this moving object must be equal to the amount of energy used to accelerate it to that speed (friction,etc aside). Therefore, this formula also suggests how much energy it would take to accelerate an object to a particular velocity. But, it then also implies that the amount of energy required to accelerate an object increases exponentially as the speed increases, very quickly towards infinity. It would take far far more than twice the energy to double the speed, but I don't believe this is what actually happens. (in special relativity, when more energy is required to accelerate an object, it is described as the mass increasing with velocity) What am I missing here? Thanks.