Brakes won’t make any significant difference on mileage. Except that, if you come to a stop versus a slow roll the engine has to work that much harder to accelerate. Which is why highway mileage is better than what you get in town.
Engines require a combination of air, fuel, and spark to make explosions. The faster you accelerate, the more air and fuel is needed by the engine in order to make a bigger explosion which is the energy used to crank the wheels. Hence, worse mileage.
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