An email I wrote to my AP Physics 1 class after their second problem set

We didn't do great - but we never do, on this problem set.  The two questions I'm addressing here are based on the graph below, where they were asked to calculate an instantaneous speed at t= 4 s, and where they were asked what familiar object might perform this motion.  

Please read on, 'cause there's an extra credit word buried here.

1. The instantaneous speed is given by the slope of a tangent line.  That means draw the tangent line, and take the slope.  That does NOT mean to just divide the y value by the x value!  Just because speed is in units of m/s does not mean you can divide any old m by any old s!  :-)  Look below - the black line is the tangent line at t=4 s.  The green and blue show how I've calculated the rise divided by the run.  NOT 22 m/4 s= 5.5 m/s!  But see the calculation below:

2. Yes, a cart, an airplane, and a rocket can all speed up, slow down, and turn around.  But look at the vertical axis.  This object goes 50 meters (60 m - 10 m) in 8 seconds!  My tracks are only 2 meters long.  A football field is about 100 meters long.  (For the Americans, a meter is about the same as a yard.)  So if it takes eight seconds for an airplane to go half a football field, well, that's not a very good airplane.  (Unless the airplane is taxiing, but then the speeding up and slowing down and turning around are crazy!)

I'd think a bicycle... start at the goal line and speed up, slow down as you approach midfield, and turn around.  But anything with a reasonable discussion of how long it takes to go several dozen meters is fine.

(Not a roller coaster... remember, an object in these graphs can only go two directions, toward or away from the detector.  The graph isn't a picture of the track that the coaster is on!)

3. If you would like an extra point on Wednesday's quiz, please write the word "astonishing" on the quiz.  While you may not share this word with anyone - make them read the email themselves! - you may encourage other people to read this entire email.  :-)

I'll see you Wednesday!  Keep writing facts!

GCJ