Leopold, what you're saying is that emergency braking will not prevent a collision since if only activates when a collision is "unavoidable." It can't make an unavoidable collision avoidable.
This was discussed elsewhere. First, AEB is not 100% effective. It is a collision mitigation mechanism, not a collision avoidance mechanism. Sometimes it may not even mitigate the collision (when it fails to detect an imminent collision for whatever reason).
It makes a huge difference if you hit someone at 30mph, vs. 10mph (it is 9 times better at 10mph). So even some braking is good.
It WILL sometimes work, but remember it does not have to worry about human reaction times when applying the brakes. It knows how long it takes to stop (assumes ideal dry conditions I suppose) and will wait until the very last moment necessary to apply the brakes.
I would read the entire section in the manual. There are a LOT of caveats.
This is the previously referenced article:
Automated-Emergency-Braking Systems Don't Always Work - Test Results
I don't think there is any feature called FAP.
I know, you meant EAP...
FCW should alert prior to AEB, so set that to maximum sensitivity. I don't recommend testing it specifically; eventually a situation will arise where the warning will trigger in your normal driving. In theory, if FCW goes off, the car SHOULD soon thereafter emergency brake to mitigate (possibly not avoid) the collision. Do not test it.
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Regarding the cruise control braking...as the article above describes, it will brake for TRACKED vehicles (I don't mean tanks...). Untracked vehicles, not so much. Please do not expect it to brake for untracked vehicles (also don't expect it to brake for tracked vehicles...). These tracked vehicles are indicated on the screen as a darker vehicle (I think). As indicated in the manual, there are also a lot of caveats with respect to TACC and when it will be effective at tracking the leading vehicle's speed.
These features are all Advanced Driver Assistance features, and you should not
expect them to avoid any collisions. They are meant to cover SOME situations where you are somehow surprised/distracted/incapacitated (possibly through no clear fault of your own). These situations are one of the most common causes of accidents and injury/fatalities, and these features when properly implemented can drive down those accident & property damage rates. There are balancing effects which drive up rates, however, when people begin to rely too much on the systems (avoiding this is part of "proper implementation").