Dude, what the car sees as stationary wouldn't be an object in front of it where the distance doesn't change, the car would know that means it is actually something that is moving at the same rate of speed as it is. An object that is getting pinged by the radar as approaching at close to the velocity of the car is what the car sees as a stationary object. How you don't get this when you specifically mention police radars being adjusted to take into account the police cruiser's own velocity is a little mind boggling. As others have mentioned, the car ignores stationary objects because they could be a variety of different objects (road sign, soda can, trash can, even a car in the next lane that is stopped on a curved road, or a car that is stopped in a lane over while you're changing lanes) and relies on driver input. At a determined distance where it's clear the object isn't any of these, that's when AEB kicks in for cars with only radar, which is why most (all?) manufacturers have language in their safety system descriptions that the AEB mitigates crashes and generally make no mention of it completely preventing them. Cars with cameras can use image processing to supplement the radar, but even then it isnt super reliable as of yet.
Like I said, a radar sees an approaching object approaching at the speed of the vehicle. If the vehicle in front of your is traveling the same speed as you are traveling, it is stationary.
If you are driving at 70MPH and you approach a car doing 50MPH, the radar sees that object approaching you at 20MPH.
Now, a radar can be programmed to ignore an object approaching you at 70MPH if you are driving 70MPH as that velocity would indicate a stationary object. But that is not how the radar sees the object. The radar sees the object approaching at your speed.
That you are unable to Google a simple search on Doppler Radar and read how it works is mind boggling.
That you completely don't understand how a radar works is understandable, but a vehicle radar used for Adaptive Cruise Control or AEB system will ignore a return from a soda can or a very small object like a waste basket. There is a threshold programmed into any radar, where a return scatter smaller than X is ignored. And for a good reason. If a radar responded to every soda can and road debris, the system would be effectively useless. They simply use a signal threshold filter where smaller objects are ignored.
However, most cars are pretty flat on the back, and provide and excellent strong return signal back which the system would use to respond to.
The AEB system calculates the velocity of the object and the estimated brake distance, and responds accordingly if the driver fails to react in time.
As noted however, a radar can't effectively respond to radar scatter that is above or below the object, or if they are using Lidar, it would rely on something reflective, as Matte objects, such as a dirty car, don't reflect those quite as well. Which is the same reason cops use your headlights or front license plate when using Lidar.
There can be multiple reasons why stationary objects present a problem for the system however, the #1 probably being an insufficient response time for the system to respond to something approaching you at that speed.