Your story got me curious, so I cracked open the owner's manual and went for a test drive. Mainly because I don't recall the parking distance ever activating while pulling behind another car at a stoplight.
Per the OM, the system activates below 2.5 mph, and the front sensors only registers objects at distances less than 24" away.
What I observed was a slight delay in the system kicking in once I slowed to the threshold speed. At 2.5 miles per hour, the math says it takes 7 seconds to close that gap, but in reality it felt like no time at all. It was hard to get the system to activate without purposefully controlling my speed with the brake while approaching the car.
But it also felt like, at that speed, it would just be a light tap resulting in superficial damage. With your ACC active, I'm betting your car already accelerated beyond the threshold speed before you were within 24 inches.
I experimented with pressing the Parking button while driving. All it did was activate the self-parking system at speeds above 2.5 mph.
Perhaps most importantly, the PDC system is definitely not connected to auto braking. So even if you met the 2.5/24 conditions, you would have at best got a moment of tone to react to before the collision.
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