I've been confusing myself over how much energy it takes to accelerate a vehicle (assuming no friction/air) with a given amount of fuel. I know that the amount of energy required to reach a given speed increases quadratically, but does the amount of fuel required also increase quadratically? Or does the amount of energy taken from the fuel increase over time? I'm pretty sure this is me confusing impulse with energy, but I don't know the relevant details of how a car works to begin with. For example, you press the gas the same amount and for the same amount of time to go from 10 to 20 as you would to go from 50 to 60 (so same impulse). Does it use the same amount of fuel?