With the example of the car on the road then, the car does use more than twice the energy to double the speed, right? Not only does the motor have to do the exact same work all over again, but it also has to do it at twice the output rate since the gearing is twice as tall. With taller gearing...
But the energy output of the battery is no greater than it was before. It makes sense that the distance is 4 times greater, but the energy from the battery doesn't match the energy required mathematically.
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...