Trip to the Big Game

This is a graph of a trip to the big game. It starts with a planned route that includes some time at a party before the game starts.
  1. Click the advance button (double right arrow ). To see the average rate for this trip. The planned average speed is distance divided by time or 50 km/hr.
  2. Unfortunately the traveler did not leave at the planned time and was caught in a traffic jam. So they used a revised route and skipped the party . Click advance
  3. The traveler was stopped by a police officer. Click advance.
  4. The traveler showed the officer that their average speed was the same as for the original planned route of 50 km/hr. Click advance. The officer however insisted on using the instantaneous speed that they measured of 200 km/hr and gave the traveler a speeding ticket.
This story is about the difference between average rate or average speed and instantaneous speed. The officer was not interested in the average speed of the traveler. The ticket was based on the instantaneous speed. The officer actually did not measure the instantaneous speed but measured the speed based on a very small distance over a very small time which was very close to the instantaneous speed.