For a few months back in the 80s I used to drive every day from Bristol (UK) to Aylesbury and back. 110 miles each way, mostly along the empty-ish M4 motorway, so I wasn't hanging about.

Most early mornings when I passed the Bath junction there would be a cop car parked on the entrance ramp as I flew past and one morning he started after me. I kept my foot down and he didn't catch up with me until I was slowing down for the Oxford exit. Going down the ramp he pulled alongside me and when we both stopped at the roundabout below the guy in the passenger seat wound his window down, smiled and said "Good morning"...and they drove off. Didn't bother coming after me again.