After about 3 years of learning physics, I still can't understand how the kinetic energy formula works. If the velocity of an object is doubled, why does the energy increase by a factor of four? Here's an example where this theory breaks down for me: I have a stationary object in space. To accelerate this object I have some sort of propulsion method which is powered by a battery. Lets say I accelerate it to 10m/s. This would require energy from the battery over a period of time for acceleration. Ok, so I drain the battery to half empty accelerating it. Now I want to double its velocity to 20m/s. The remaining half of the battery should be enough energy because the object is accelerating in the same way over the same period of time. So why is it true that I need 4x the energy to accomplish this? Is my example not possible? Am I missing something?