The story

These two graphs represent my quest for dinner in Sacramento. I left my home in West Sacramento to go to the Spaghetti Factory in downtown Sacramento. On my way to Route 160, I encountered two stoplights (see zero velocities at time 1.25 and time 1.75). My assistant proceeded onto the ramp for Route 160 (see increasing speed around three minutes) and drove a steady 55 mph for about 45 seconds. Then, at a little over 4 minutes, there is a decrease in our speed as we crossed the tower bridge into Sacramento. From 4.75 minutes until 5.25 minutes, we sat at the stoplight by the bridge. After this we drove down J Street at a moderate speed (20-30 mph) toward the Spaghetti Factory. At around 10 minutes, as we neared the Spaghetti Factory, we decided that the wait looked far too long, and that we should go to the Good Earth instead. At this time, we drove back toward Route 160 and increased our speed until my accomplice got a little out of hand at 70 miles per hour (luckily no CHPs). Then, we exited at Arden, our speed decreased to zero two more times as waited for traffic lights. Finally, at time 19.00 we parked in the Good Earth parking lot and headed off to our dinner.

It is difficult to note from these graphs that velocity is the derivative of position. I believe this is because the velocities were taken at 15 second intervals and could only be approximations of the average speed for that interval. At points, however, this relationship is very clear. For example, when the position does not change over time (at stop lights) the velocity is zero. This makes a lot of sense. Also, when the position increases rapidly, such as from time 2.00 to time 4.00, the increase in velocity is apparent.