How does the frequency of a cars returning radar signal change if the car moves away from the radar source?

The frequency of the radar signal does not change. Be it a cop getting you speed, or a modern car with Brake assist (they use a radar signal to assist keeping a safe distance) it's all timing, how long from the radar source to return to source. If a police car is still, and you are moving away, the increase in return of signal time tells the computer in the officer's car your speed. Even if you are going toward each other, the computer knows the speed of the officer's car and again, signal return time factored in with speed of cop car the computer can give an instant, real-time speed.