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Why is it more fuel efficient to accelerate briskly to a safe cruising speed in a car?

This website http://www.advanced-driving.co.uk/driving-tips/acceleration-sense/ said that this is one of the pillars of fuel efficient driving but it didn't really explain why. It seems like accelating briskly would use up a lot of fuel in a short period of time to overcome the low inertia that the car already has.

Public Comments

1. accelerating briskly gets the momentum moving quicker. like pulling a tooth. don't want to wiggle it or finesse it, you just want to yank it out ASAP. a car slowly gaining speed will use more gas trying to get the momentum moving to the point where it can coast. jac rabbit starts or gassing it from the beginning will get it to the coasting point quicker and let you ride it out rathen than continually accelerating
2. I disagree. Getting into the top gear asap and stepping on the "go" pedal gently works best.
3. If someone is advising ropming on it to quickly get to cruising speed, ask him which of his petroleum company's stocks are currently paying the greatest dividends.