Can a cop car clock u more than a hundred feet away going in the opposite direction?

[Calvin R]

i was traveling north bound and the officer was traveling south bound, i had just came back from getting my car from the impound.i barely passed the check point of 50 mph. The officer clock me going 63 mph. the officer was more than a 100 feet away coming toward me. There was traffic in the area. when i looked a my speedometer it said that i was at 55 mph. then i turned and thought to my self he's going to pull me over, i was being paranoid because that early morning i got a DUI. ok so, coming in the opposite direction about 10 seconds after i said it he turned his lights on and did a U-turn and stop me. he ask did i know what speed i was going i said 50 and he said 63. prior to being pulled over and getting my car back i went to the police department to pay them to get my car out. the reason being is because around 2 a.m. of that day i got a DUI. so, my question is can this be a done on purpose to give me a speeding ticket, because I already been to the police department? Also, is it possible to be couples miles away from someone and clock them speeding in the opposite direction being possibly more then 3 miles away? lastly before the officer tuned his lights on i was at 55 mph and he was more than a mile away in the opposite direction.