Average speed conceals waste. Two cars can cover the same distance in the same elapsed time, yet consume different amounts of fuel because that average says nothing about their bursts of acceleration, speed peaks or braking. The distinction is physical. Fuel pays for the entire sequence of motion, including energy that reaches the brakes rather than carrying the car farther.
Braking can squander progress. Whenever an engine accelerates a car, it adds kinetic energy, which increases with the square of speed; friction brakes then convert much of that energy into heat when the car slows. Anticipation changes the bill. Easing off the accelerator early for a red light allows existing motion to cover distance that another driver might cover under power before braking sharply. Speed peaks cost extra. Aerodynamic drag rises roughly with speed squared, so racing between stops can increase losses even when both journeys take exactly as long.
Gentleness alone guarantees little. Engine efficiency depends on load, engine speed and gearing, so an excessively slow acceleration is not automatically better than a moderate one that reaches an efficient gear sooner. Avoidable braking matters more. With comparable vehicles and conditions, the economical driver generally avoids unnecessary acceleration, leaves room to anticipate traffic and slows safely without chasing every opening. Hybrids soften the penalty. Their regenerative braking recovers some energy, but conversion losses mean that avoiding an unnecessary speed change still has value. At the red light, haste has become heat.