Suppose you are driving along a motorway exceeding the speed limit, and you notice a cop with a speed gun aimed at you and he/she is about to take a reading of your speed. You jam on the brakes, and the reading is actually taken as you are deccelerating. How is the reading on the gun affected? Could it appear that you are below the speed limit when in fact you are above it?
This question remind me of the way Prof. Dan Kleitman at MIT says he once tried to beat a speeding ticket: he claimed in court that the radar gun was (or could have been) at least partly aimed at the very top of his tire, whose velocity in the forward direction would be TWICE the velocity of the car, leading the radar gun to overestimate his speed by a factor fo 2. Kleitman's theory didn't convince the judge, and he ended up having to pay the speeding ticket, but it's still a good story, and one that's fun to tell at the start or end of a calculus class. There's a nice way to see that when a wheel is moving forward with velocity v, the top of the wheel is moving forward with velocity 2v: use the fact that the hub is always midway between the top and bottom, and the fact that the bottom of the wheel is moving forward with velocity zero. Jim Propp