Does the amount of fuel needed to accelerate a vehicle increase quadratically?

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SUMMARY

The discussion centers on the relationship between fuel consumption and acceleration in vehicles, specifically whether the amount of fuel required to accelerate increases quadratically. It is established that while energy requirements for acceleration increase quadratically, fuel consumption does not follow the same pattern due to varying efficiency at different speeds. The conversation highlights that more power is needed to maintain the same force at higher speeds, and that optimal fuel efficiency occurs at specific speeds, typically around 45 mph for medium to larger cars. The nuances of impulse versus energy and the impact of engine load and RPM are also addressed.

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  • Research the principles of vehicle dynamics and acceleration forces.
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Alkatran
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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?
 
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Alkatran said:
For example, would 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).
No, it would take more pedal pressure or more time to accelerate from 50 to 60 than it would from 10 to 20. Ignoring aerodynamic drag factor, power = force times speed, for example, horsepower = force (lbs) times speed (mph) divided by 375 (conversion factor). So even if the force is the same, the speed at 50 is five times as much as it is at 10, so it takes 5 times the power to generate the same force at 50 as it does at 10.

On the other hand, a typical gas engine is most efficient at a certain load and rpm. A typical medium or larger sized car gets it's best milage at around 45mph, a combination of gearing, rpm, and engine load.
 
What about in a frame moving at 50 watching the car go from 50 to 60 (maybe we should use a rocket, since then the wheels won't give away the speed)?
 

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