I closed up a unit in calculus on position/velocity graphs. Most of my students had horrific memories of physics their freshman year. That teacher, needless to say, is gone. Last year, a number of my calculus students just shut down when we encountered this topic.
This year, I focused a lot on the concepts. One day I showed dy/dan’s graphing stories and that night, I had them each come up with their own problems. For these problems, they needed to draw the velocity versus time graph and the position versus time graph.
Initially I was going to use my favorite on the assessment, however, there were so many hilarious, exemplary problems, I had to type them up and spend the next day using them.
Some of my favorites:
1. Dare-devil Mr. Shah one day decides to go Bungee Jumping. At the top of a mountain, scared, he hesitates 2 seconds, then jumps. He [falls] quickly, eventually reaching terminal velocity at 100 m/s . At the bottom the rope reaches its limit pulling him back up, [coming] to a stop. Mr. Shah smiles.
2. Mr. Shah is riding the elevator to the 4th floor. He waits for the elevator for a bit and then gets on. The elevator goes to the basement to make sure no one is waiting down there [and, of course, no one is there, as always]. It quickly goes back up to the first floor, where 15 seniors try to crowd on. When everyone is in the elevator it heads up to the 4th floor stopping at the 3rd floor to let people off. Finally Mr. Shah reaches the 4th floor and comes over to our calculus class.
3. The Jonas Brothers are walking down the streets of New York City at a strolling rate of 2 mph for 10 minutes as they composed a new song. Suddenly, [student 1] and [student 2] began running at them screaming, at 7 mph. Struggling to find a hiding spot, the brothers run down the block at 8 mph for 5 whole minutes, when they lost the crazy groupies-in-training. Stopping for a break, the boys catch their breath for 5 minutes on a stoop. Walking away when the coast was clear at the same strolling rate as they began with, Nick remarked, “Sorry guys. I’ll try to be less attractive.”
4. A helicopter is taking off. It rises constantly at 200 ft/minute. After rising for five minutes. It stops for one minute to survey the surrounding area. After rising again for 2 minutes, the helicopter is abruptly blown up by a terrorist missile.
5. A man runs from a tiger going at a constant velocity of 3 mph for 1 hour. The tiger gets tired so the man catches his breath for 20 minutes. A rhino appears and begins to chase again and the man picks up speed to 5 mph.
6. You are in an elevator on the top floor (6th floor). Each floor, it picks up more people and it goes slightly faster each time. When it stops on the 2nd floor, so many get in that it breaks and crashes to the basement. People die.
This was a fun class. And almost all my class got pefect scores on the conceptual part of the latest assessment, on this material. They got it1 They really got it!