Braking = getting rid of energy, aka gas. Coast more, brake less, save gas.
Hard acceleration = high engine RPM. Slower spinning engine means less energy lost to friction.
Both of these in moderation. Most of the energy saved in coasting is at high speed. 60 -> 40mph is worth more than 40 -> 0 mph. Accelerate too slowly, and your car spends extra time in lower gears where it has more engine speed.
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