"Fuel consumption is fundamentally related to the forces of acceleration and braking"
I'll stop you right there. No it isn't. Clearly the goal of good economy relies on the preservation of momentum, but the instantaneous 'g' force is not relevant.
If I brake sharply-but avoid stopping, I will use less fuel than someone who brakes gently to a standstill.
The same goes for acceleration. Crawling away from the lights feels virtuous, but is actually selfish because fewer cars get through the lights which means more congestion and poorer consumption for everyone else. The energy required to accelerate a mass from rest to a given speed is essentially constant irrespective of the rate of acceleration. The engine is more efficient under load, but the amount of tyre slippage will increase.
The key is anticipation-which means looking at the road ahead and not at a 'g' meter. Sorry
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