I really want to point out a hole in braking theory that bugs me every time I hear it.
It is bandied about, supported by much the same notion of exponential braking as you mentioned Aido that you drop around a quarter of your speed in the last five meters. That just does not stand up to any thought.
Scenario A, panic stop from 60KMH, in the last 5 meters you are carrying and stopping from around 15kmh.
Scenario B, same car, panic stop from 100KMH, now using the logic bounced around about the last 5 meters you will apparently be able to stop from 25kmh. Why can't the car stop that hard from 60?
It just does not stand up to any scrutiny at all. I also do not agree that braking is exponential, it is nearly linear. That is backed up by data logging from my own race car. The longditudinal G force produced in hard braking is pretty consistant from start to end, that means your retardation is prety consistant from start to end, in my case it fell off slightly towards the end of the stop as the car actually does produce some downforce at speed so some grip is lost as you slow down and if you get it perfectly right you will actually loose LESS speed in the last 5M than the first 5M of effective braking. It is as simple as time multiplied by braking effort. I also loath the reaction times they quote when producing stopping distances. I think the typical time they quote from seeing an obstacle to applying the brakes is 2 seconds! Anyone who takes that long to brake needs to concentrate more, and if that really is a typical reaction time then they need to be doing something about it.
While I do agree that for any given scenario, a lower starting speed means a shorter stopping distance and more chance of not hitting any obstacle, the advertising is also pretty misleading and selective. Yes in the TAC scenario from 50KMH you will bump the girl who walked out in front of you and bruise her knee rather than cleaning her up at 55kmh. You can carry that on ad infinitum justifying a lower and lower speed until the dopey bugger bruises her knee when she walks without looking into the side of your stationary car!
I think that is just another aspect of what has been mentioned above and I have drawn this out of people I know in discussion. After 20 years of TAC ads all some folks I know think you need to be safe is to drive within the speed limit, not drink and drive, wear a seatbelt and at a stretch they might admit that not driving while fatigued could be a good idea.
I am ex Air Force and a safety poster aimed at pilots (I was not one, I was a techo) said it all about the current TAC and govenrment thinking, they could really learn from this.
"Spread your attention, dont focus on detail"
Applies to driving a car and my thoughts on the current Government approach to road safety equally well and is equally poorly adhered to in both cases.