If an object at rest has, say, one constant force “forward” on it and the object’s mass isn’t changing (and we’re not getting relativistic) then the object will have a constant acceleration. That means its velocity increases in a linear fashion. However, that means its KE increases quadratically. So, it seems to me, the object is gaining more KE every second than it gained last second. (More KE is gained going from 2 to 3 m/s than from 1 to 2m/s.) That means the power from the force is increasing, even though the force is not.

Something I was reading said this makes sense because the object has a greater velocity when travelling fast, and therefore covers a greater displacement each second, so the work done each second is more when you are travelling faster since d is bigger (during each second) and Work = F*d (is true in this simple case with a constant force and since the angle between F and d is 0).

I’m pretty sure about all that, but if you find a flaw fine. But here is my question:

If the force needs an increasing power, does that mean that, say, a car or rocket (ignoring the rocket’s changing mass) needs to burn MORE fuel each second to maintain a constant force when it’s travelling faster than when it’s travelling slower?

I would’ve said before that burning fuel at a constant rate provides a constant force, but now that seems impossible. Burning fuel at a constant rate means a constant rate of energy consumption and thus a constant power (right?), but an INCREASING power is needed to keep increasing the amount of kinetic energy gained each second.

Please help untie the knot in my head about this. I feel like there should be an easy explanation to it but I’ve asked a few sciency people and they couldn’t reconcile the situation for me. As you answer: I’m a high school physics teacher and I know my stuff, though I’m rusty on things like the Hamiltonian and “past” that. I know the whole question breaks down at high speeds, and Newton is wrong, Einstein is (probably) right, but let’s try to pretend this isn’t a question about relativity (assuming that’s possible).