How far away are we talking about? I believe most automotive radars reach out either 100m/330ft or 200m/660ft - so it won't be seeing anything beyond that.
Part of the problem is the radar doesn't understand "car." All it knows is that something on a particular bearing and moving at a particular speed is reflecting radar energy at some intensity.
That's why the easy solution is to drop any return that appears to be moving within a couple percent of the car's current speed - letting out all of the road signs and bridges and guard rails and rocks - and also stopped cars.
To reliably identify stopped cars, you need more information - either something else to say "there's a car on this bearing, tell me about it" or "our car will be driving along this curved corridor, tell me about anything within this combination of bearings and ranges" (which will still need some help when it comes to bridges and overhead signs, since AFAIK all car radar is two dimensional.)
That's where the sensor fusion comes in - either using image recognition to identify the cars, or at least feeding the corridor back to the radar.
AFAIK, closing rate (and bearing and range) on all returns is calculated ~20 times per second by the radar unit - that's how it is deciding what's relevant and what isn't.