It helps to re-frame the premise. An object which has a constant force applied will have it's distance increase quadratically with respect to time. Energy is

It helps to re-frame the premise. An object which has a constant force applied will have it's distance increase quadratically with respect to time. Energy is force times distance. Intuition: the energy it takes to lift an object up is proportional to the height you lift it to. So if you apply a constant force, you get a constant acceleration which leads to a quadratically increasing distance. If you accept that energy is force times distance, the energy required to move the object in this scenario increases quadratically. This means that if you apply a force F for 1 second, the amount of energy that is imparted by that force depends on how fast the object is already going. The energy required to apply a force to an already fast moving object is much higher. Intuition: you have to expend all the energy required to get up to the moving object's speed before you can start applying a force. So there's a cost to even get in the game