Well they just told you a blatant lie in driver's ed.
Cops can and will pull you over for going 5 miles or less under the speed limit. Contrary to what driver's ed may have told you, police will even be instructed by their chief to do so - especially if they haven't given out many tickets that month.
The county, the courts, the police, and the governments all know and recognize that tickets mean cash-flow for the county. It's not about whether you are guility or innocent - they could care less. It's about money. Take the police officer to court and try arguing that you are innocent. The cop may even lie right out of his teeth.. and the judge knows this. But will not care because it's all a system for generating money that they have been through a thousand times.
Look on the back of the ticket. Do you notice how above all things, they make quite clear where and how to send them $ for the fines? If you try to fight the ticket and lose, they will emphasize where and how to send the money for fines, charges, etc.
Police are given a quota direct from their superiors and must give out a certain number of tickets. If they give out a few tickets for a month, they can get written up. This means that if they are falling short of the quota then they may set up a speed trap or give out tickets to those who don't deserve it.
Also, to answer someone else's question regarding why the police officer won in court when he did not even have a radar reading. It happens all the time.
There is a law that states that police officers are now able to guess someone's speed legally within 5 miles an hour. This means that cop could see someone drive by in a 45 mph zone and use his amazing sense of speed to determine that he must've been going 70 mph. It's a guess, he has absolutely no clue, but you can and will get a ticket for it. Because the police officer could be off by 5 miles per hour (which would then mean you could've been going 65) you can still get the ticket, because that would still place you above 45.
He does not need a radar, vascar, laser, or photo reading anymore. Because he is legally allowed to guess within 5 miles an hour of the speed and his word is the best evidence in this case.
But, do not worry. There's no reason why you can't beat him. Disprove the cop's ability to determine speed accurately. Drop a pen on the ground. Ask him if he knew how fast the pen travelled before it hit. Drop different items. Figure it out ahead of time mathematically how fast it travelled. The cop will have no clue.
In the event that you try to fight the ticket and take it to court. If  the cop says he had a radar/speedometer reading that says you were going a certain speed. The judge will ask you for your testimony about what happened. Do not say a word. You are the defendent, you have the right to remain silent, anything you say in court will be used against you. The police officer is the prosecutor and it is his job to prove that you are guilty. Do not make his job any easier by opening his mouth.
The high courts have ruled that radar is a legal and accurate method of determining speed - providing that
1.the police officer has completed courses on operating radar (and has proof of it with him at the time of the trial)
2.has had the radar gun inspected and checked to be operating (and has proof of it with him)
3.Calibrated the radar gun before and after your ticket (and has proof of it with him at the time of the trial)
^however, if you do not ask the right questions this will be ignored because the police officer's testimony will be used as the best evidence. The judge may tell you that the documents are not necessary and that the police officer's word is good enough.
It's not. That's bullshit, and the judge knows damn well it is. This is where you kindly grace the judge with a copy of case law and the high courts ruling. He can not ignore it. He knows that if he does, you can appeal it and take it to the high courts and his name will be on the line. The police officer will be forced to show the documents that he does not have. You will win.
I will tell you that last year I was going over 90 mph. I ran from the cops. I ran stop signs. I received a huge speeding ticket. I was guilty as can be. I took the ticket to court. I won.
It's not about being innocent or guilty. It's whether the cop can prove it.
I have seen police lie in court time and time again and get away with it. Don't lie, don't make up any stories, and even if you are in the right don't tell the judge anything. The second you open your mouth and say 'I wasn't going that fast!' you will be found guilty. But, if you approach it like I have said earlier, you will win.