Police Perpetually Stuck Behind Me

I was wondering yesterday if police officers always get annoyed by having to drive behind slow people. I was driving behind a police car (actually two) with another car in front of them. Most people drive the speed limit when a police car is behind them. That means that whenever a police car is behind someone, it is going to have to go the speed limit. From the police car's perspective, it is like they are always behind me. I figure that must be really annoying. And to confirm that the police car didn't want to be going that slowly, I watched as the car in front turned off and the police car started going much faster.