At what point in the braking operation does the system give your car the maximum stopping distance?
You meant the SHORTEST stopping distance? Dry level road, good & well-inflated tires, suspension, alignment and brakes in good shape, but above all: speed and (human) reaction time.
Braking performance is dictated by the power of the braking system and the grip of the wheels. assuming yur brakes are strong enough to cause the wheels to lock up when applied hard at any speed, maximum braking happens right before the wheels lock up. wheel lock up happens when the brakes apply more force onto the wheels than they can provide friction with the pavement. this causes them to slide. kinetic coefficients of friction are lower than static (sliding things are less grippy than non sliding things). because of this, once the wheels start to slide and stop spinning, braking performance will be drastically decreased. because of this, you want to maximize the force applied to the wheels without having them slide. this is why maximum braking performance is achieved when the right before the wheels lock up. for most drivers this can be a very difficult skill to master especially considering that most extreme braking is done to avoid accidents. in these cases the driver has very little mental preparation to be able to maximize braking and many people end up just slamming on the brakes and sliding away. ABS systems work by sensing wheel lock up and then pulsing the brakes on and off very quickly. this lets the wheels regain traction rather than keep sliding. this means that for most people, maximum braking comes by pressing the brake pedal the hardest possible. this is so that the ABS system kicks in and takes over. if there is no ABS system, this type of braking input can easily cause the wheels to lock up and decrease performance.