I have learnt that the kinetic energy of a moving object is equal to its mass multiplied by it's velocity squared, divided by 2. If I takes off in my 2 million kg spaceship from rest to 1 million metres/second, I have calculated from this formula that I will need 1 million, million, million Joules of energy. However, to achieve a velocity of 2 million metres/second, my 2 million kg spaceship will need 4 million, million, million Joules of Energy. Is this correct? This confuses me... Asume that Harry and Burt both get into a space ship for a trip out into space. They are both given an instruction to accelerate the rocket to 1 million metres/second. At launch Harry goes to sleep and Burt takes off. As per his instruction Burt accelerats the ship to a velocity of 1 million metres /second. Burt then retires for some sleep. When Harry wakes up, he thinks the ship is at rest, when in actual fact it is travelling at a constant velocity of 1 million metres/second. Following his instructions he accelerates the ship to 1 million metres/second relative to his initaial velocty. If my thinking is correct the final velocity of the rocket ship is 2 million metres/second relative to the initial starting point.??? Now, for such a trip I calculate the Burt used 1 million,million, million Joules of energy. Since, Harry. had exactly the same instruction as Burt, then Harry used 1 million, million, million Joules of energy, too. Adding the two together, total energy used is just the sum of the energy that Burt used and the energy Harry used which is 2 million, million, milllion Joules. However, how can this be since the ship is travelling at 2 million metres/second and has a Kinetic energy of 4 million, million million Joules. What am I doing wrong here?