While gentle driving will in most cases save fuel in a diesel, it may not be true for a petrol engine.
Diesel engines run very very lean. By touching the gas pedal, all you do is making the mixture more rich by injecting more fuel. The air taken by the engine is always the same. So by being as gentle as possible on acceleration, you can save lots of fuel in a diesel by keeping the mixture lean.
With a petrol engine, the more you open the throttle, the more air AND fuel get in, increaing the pressure and most of the time increasing the temperature inside the cylinders. The higher the temperature, the more efficient the combustion (
http://en.wikipedia.org/wiki/Thermal_efficiency), the less fuel you use. So by flooring the gas pedal, you get the most efficient acceleration. BUT newer cars will also enrichen the mixture if you floor the gas pedal (to deliver much more power), making you lose any potential gains from the increased temperature. So try to accelerate with 50-75% throttle. Don't floor it and don't baby it.
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