In this particular scenario, the officer was reading the driver's instantaneous velocity at an angle to the vehicle's path. In other words, the officer had a different frame of reference, which ultimately changed the radar gun reading.
Ladies and Gentlemen, I would like to bring up a relevant detail in Bob's case: relative velocity. It all has to do with frame of reference, which varies with the observer's position and his/her relativity to the object observed.
It is worth mentioning that the only way the device could have accurately recorded the instantaneous velocity of the car is if the police car was directly in front of the car as it accelerated. However, the police car was on the side of the direct path, and thus, the driver is telling the truth.
Wow. I almost fell asleep during that monologue. In fact, I believe that you just proved my point. The radar gun effectively measures the car's instantaneous velocity by using radio waves! Therefore, my reading of 110 miles per hour was accurate!
The speedometer on your car also displays instantaneous velocity. Therefore, your actual velocity at that given time was equal to my radar gun reading.
Oh, but wait! You didn't let me finish my argument. Allow me to present an expert physicist who has made groundbreaking discoveries in physics and engineering: Archimedes!
Good Afternoon honourable judge and dignified jury. I am here to talk about relativity.