Yeah, it's insane how quickly it happens. I was rushing home from work (in an unspecified Midwestern state), speeding on the highway because I didn't like the weather that'd formed while I was getting gas in my old truck. It was maybe 5:00pm but getting unusually dark behind me (out the back window), so I was easily doing 85+MPH on a 55MPH highway out on the plains.
I looked back and suddenly saw the red & blues and alternating headlights of a police cruiser, and knew I was cooked (there was no hiding or denying my speeding). I was preparing myself for an arrest for reckless driving and already had my signal on to indicate I was pulling over ... when I realized he was easily doing 100+MPH and running like hell himself. Blew right past me, gesturing (I think) to me to get a move on.

I floored it and kept going. That old beater had no hope of keeping up with a Crown Vic, but the fucker gave it a good college try anyway. After he passed me, I looked in the rear mirror one last time and just saw nothing but total darkness. I quit looking back and just concentrated on "GO FORWARD GO FAST DON'T LOSE SIGHT OF THE COP." Didn't stop until the sun came out again.
Found out the next day the two of us had narrowly avoided a fatal encounter with an F4 that crossed the highway right about the same spot where he passed me. If he'd actually pulled me over for speeding, we'd have almost certainly both been killed.
Thanks, btw, Mr. Random Based Police Officer for not being a dick to a teenager trying to outrun a tornado in an old pickup truck.