The speedometer in this video is broken.

Can you (or your students!?) fix it? Be careful: there are a couple of interesting ways to get this one wrong.

Also: what would the graph of speed v. time and position v. time look like here?

Let us know how you’re thinking about it in the comments.

2015 Oct 17. Updated to include the answer video and answer graph. You can also download these files at 101questions.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. #### Nick Hershman

October 16, 2015 - 11:10 am -

My only thoughts about how to ‘fix it’ would be to key through the video frame by frame and pick some stopping points. Is there a way to do this w/ youtube/vimeo without storing a copy of the video on your local hd?

Anyway, if you can key through the video one frame at a time and have accurate reading on the video time, then students can record exact time and best guesses at the position on the field and plot time v. yard-line. Might generate some interesting discussions when we calculate speeds between neighbor points on the graph (somewhat approaching instantaneous velocity) and by skipping a few points (giving an idea of avg. velocity).

This task feels a little contrived to me though — I would expect a student to suggest just searching for the unedited video. The task is imposed on students by removing information that anyone who saw the original video would have. I wonder if it would seem more interesting to leave the speedometer, and have students do the investigation I described above in order to find the speed more precisely than the on-screen speedometer. Instead of fix what’s broken, maybe can you make a better speedometer than they have or how accurate is their speedometer?

2. #### Dan Meyer

October 17, 2015 - 1:37 pm -

I guess what I find fascinating about the situation is this: someone’s job was to create the speedometer animation on the replay video. Someone had to do math to do that job. I’m just trying to put students in a place to do that same math.

In any case, I think adding a timer to this video was the right call so I updated it.

3. #### Scott King

October 19, 2015 - 8:46 am -

In what way, specifically, is it broken? I took 5yd segments and calculated speeds and it topped out pretty close to the given top speed. It was close enough that I can chalk the difference up to my ability to accurately determine the actual 5yd segment.

It is clearly not the average spped for the whole return, but it doesn’t claim to be that, it says top speed. I’d say if you wait for him to get to full speed and take a measurable chunk of yardage it’s pretty close. How close does it need to be to be considered accurate would be an interesting conversation.

4. #### Dan Meyer

October 19, 2015 - 10:31 am -

It’s only broken from the perspective that an inconvenient purple box obscures the speed after a couple of seconds. Figuring out what should be under that box is the task. (“Broken” clearly isn’t the best word here.)

5. #### Bowen Kerins

October 21, 2015 - 4:24 pm -

While amazing, it’s unlikely that someone had to do the job of calculating the speedometer. Players are wearing RFID chips now, and those locations are being recorded for the calculation.

http://www.geekwire.com/2015/microsoft-will-show-next-gen-stats-on-nfl-app-thanks-to-rfid-chips-worn-by-players/

A longer video about this play, with more timing and stats, is here: http://www.nfl.com/videos/ngs-anatomy-of-a-play/0ap3000000556387/Next-Gen-Stats-Anatomy-of-a-Play-Week-5

One further aspect to explore is Alford’s 4.39 second 40-yard dash in the training combine — was he faster then, or playing with pads in the game?

6. #### Dan Meyer

October 22, 2015 - 12:27 pm -