Hi I don't understand why the relationship between kinetic energy and velocity is not linear. Consider the following situation: 1. A rocket is traveling through space at constant velocity with it's thrusters switched off. 2. The thrusters are fired at full blast for precisely one second and then stop. 3. Again, the thrusters are fired at full blast for precisely one second and then stop. If we compare the two thrustings, surely the energy expenditure and increase in velocity will be the same in both thrustings, hence a linear relationship? What am I missing in my understanding of this situation? I would be very grateful to anyone who can answer this. Thank you very much.