In my opinion, braking over a longer period is much more efficient than sudden braking. The reason is simple, and it all has to do with the fact that energy can neither be created or destroyed, but rather only change forms.
If you anticipate a stop, say, 100m in advance and decide at the very least to let off the gass and coast in neutral, then you save the fuel that otherwise would have been consumed to maintain your speed until just prior to jamming on the brakes and stopping.
If you cost from 100m out, the coefficients of friction from, just to list a few, wind resistance, road to wheel, wheel to bearing and perhaps dragging brake pads, will all naturally slow you down. These resistive forces are always acting on your vehicle, so, the faster you can anticipate a stop and let off the gas, the more gas and brake ware you will save.
When you hit the brakes, the kinetic energy of your moving vehicle is transformed into heat and noise in and around your brakes and tires. The faster you stop, the more heat and noise that is produced over a shorter period of time and distance. It’s more efficient on all of your braking components, and tires, to dissipate the kinetic energy of your vehicle movement over a longer distance and period of time. The temperatures of all moving parts don’t get as hot and therefor don’t diminish as quickly.
Its all physics, think about the opposite. What’s more efficient? accelerating from 0 to the speed limit as fast as your vehicle possibly can or accelerating over a longer period of time and distance at a slower rate of increase?
Anyway, Its Friday, I’m bored, and I can’t wait for the F’n weekend.