Acceleration is an investment in kinetic energy, one that would be best made based on results from an engine specific bsfc map. For my engines, those bsfc minima useful for charging my "inertia battery" are at moderate to high load. That coupled with my manual transmission means I have a bit of "jackrabbit starts" which is counterintuitive but works better for me. Others may have vastly different bsfc maps requiring different techniques.
The difference i have found lies in drawing down my "inertia battery" as much as possible via coasting to minimize the conversion of its energy to heat via the brakes. Thus I roll out of the throttle much sooner than most when approaching a stop. I leave additional following distance to have reaction time. Time the redlights. Know the speed you can comfortably take a turn, and the landmark that defines canceling the cruise on approach to that turn. Adjust behaviors based on weather or significant (2000lb+) loads being carried.
Yes there are times you have to slam on the brakes. Deer, other drivers, debris, etcetera. But under normal situations brake use is the enemy of fuel economy in a heavy vehicle.
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