I am going to be a little bit more technical on how cops operate speed enforcement, so bear with me:
1) Cops are trained to justify the speed of the vehicles with nakes eyes. Then, they will use speed measuring equipment to verify the speed of the vehicle and issue tickets.
2) If the cop is in the car, he will be using the on-board radar. Depend on the city, some cop cars has the ability to adjust the antenna (circle thing above side mirror) and measure speed in all direction.
Newer radar has something called the POP mode, which allows it to measure speed in less than 1 second by pulsing the radar at his/her pleasure. This is very similar to radar, where the speed measurement is instant. All radar used today has the ability to accurately measure speed while the cop car is moving. Radar has a range of over 1km (on empty road), so don't be surprise that the cop picked on you before you even know it.
The youtube video shows the popular Kustom Eagle radar that has the ability to track both incoming/ongoing traffic:
3) There is also another possiblity of the cop pacing you. What that mean is that the cop made a U-Turn and followed you for a bit without you knowing and locked radar on you the whole time. Then as you speed up, it just came out from nowhere.
4) Cops are not stupid, unless all cars looks the same. Cops are trained to spot minor things to ID the vehicle in a pack of cars.
Go dispute the ticket. Let's hope that the cop did not use any speed measuring equipment and printed the speed when it comes to the court. Based on my experience, unless you are presented by a lawyer, the court usually rules in favor for the cop when there are printed evidence along with his/her testimonies because they are the professional to do their jobs.
Last time I went to traffic court, the judge said they can no longer reduce the amount if it is at minimum. However, an installment or delay payment plan is negotiable depending on the accused situation and financial background.