20km over speed limit being charged with stunt driving?????

ok now this is scary today or yesterday night I was doing a little over 80km in a 60km zone the reason I know this is because I was staring at my speedometer I was in a rush and I can live with a speeding ticket and a cop pulls me over saying I was doing 125km in a 60km zone. I was completely shocked I told him I was watching my speed and know exactly what speed I was going that is not possible. I told him I know all about the 50km over consequences and I'm not that stupid. I ask him did you get me on radar I know he couldnt of because I know for a fact I wasnt going that speed and he says no. so I asked him were do you get this 125km hr speed from and he tells me that when he was driving to catch up to me his car was going 125km and his car was neither pulling away or catching up to me which is called pacing which is a valid form of evidence for speeding. This just happened not even 12 hrs ago and I have never felt so screwed in my life car was towed, license suspended, is this for real this is very very scary so basically what the cop told me is he can pull over anybody anytime and give them a speeding ticket or worse stunt driving ticket just because his car went a certain speed to catch up?????? I really don't know what to do and the thing that has left me so shaken is that I was WATCHING my speedometer. I went on google earth to see the distance from were he saw me drive by (I know this because he told me were he was) to the point were I was pulled over and the distance is less than 1km thats not a typo 1km. so basically he said I zoomed by him doing 125km he was at 0km sped up caught up to me and paced me doing 125km all within 1km is that even possible? I feel so stressed out right now. I'm 100% positive I'm not the only one this has happened to if this has happened to anybody else can you please chime in and tell me what the outcome was I'm definately gonna get a lawyer to fight this this is just crazy. Ive read that police cars have gps's that show what speed there were going I was thinking that might help. I think I need to hire a mathematician instead of a lawyer for this one, the distance and speeds can't add up. Another thing I want to point out that is very suspicious is that at traffic court when you take a plea deal the crown will always reduce the speeding ticket down 15km so guess what 125km - 15km is 110km in a 60 zone exactly 50km over the limit coincidence you be the judge of that one. sorry for the babling I'm just feeling pretty down and wanted to explain the story I hope alot of people see this and realize what can happen to you when you speed if it happened to me it can happen to you. I'm definatly putting a dashcam in my car right away when I get my car back next week that woulda blew the cops story right out of the water. so now that I'm finished ranting about a very bad night can somebody please chime in with some advice it would be GREATLY appreciated.