I had a similar story. I once sped through a traffic intersection and a cop car coming from the other way perpendicular to my heading. He turned immediately and chased me down. After stopping, he ordered me out and said I was doing 110mph. I was like there's no fucking way I was doing 110. The car felt very different going 110 than 60. He was saying I looked like going very fast. The only thing that ran through my mind was to get a lawyer. Amazingly he left me go after lectured me for a while. I guessed he wasn't sure exactly how fast I went.

I was wondering how can he misjudge the speed so far apart. This article explained the phonomena.