Nice free-fall data with a motion detector

On the second or third day of kinematics, after we've discussed position-time and velocity-time graphs, I introduce acceleration.  I start by handing out the four - yes, only four - facts about acceleration.  

(1) Acceleration tells how much an object’s speed changes in one second.

This is the fundamental definition, one we'll use again and again.  It leads to stating acceleration in units of m/s per second - that way, every time a student writes a numerical acceleration with units, that student is reinforcing in her or his mind the physical meaning of acceleration.

(2) When an object speeds up, its acceleration is in the direction of motion.  (3) When an object slows down, its acceleration is opposite the direction of motion.

These indicate the direction of acceleration in words students can understand.  Note that I don't use the words "negative" or "positive" anywhere!  Directions of acceleration and velocity are stated as left, right, up, down, north, south, etc.  The language used matters here.  Students may never, ever say "acceleration moves left."  Nor may they say "the object accelerates to the left."  They must state either fact (2) or (3), and conclude with "the object's acceleration is left." 

Some practice with a PASCO visual accelerometer helps here.  In the linked post, I'm using this tool to work on misconceptions about the direction of force and motion; but just stick this accelerometer on a cart on an incline, and you can have all sorts of conversations about the direction of an object's acceleration.  

(4) Objects in free fall gain or lose 10 m/s of speed every second

Once we understand facts (1) through (3), then (4) is just telling us about a special case in which we know the value of acceleration.  That's it.  Pedagogically, it's important not to treat free fall as a BIG DEAL.  Just give evidence that objects in free fall do, in fact, experience 10 m/s per second acceleration, and be done with it.

Since at this point my students are well familiar with velocity-time graphs, I like to show that the slope of a velocity-time graph will be 10 m/s per second for an object in free fall.  That's easier said than done.  Motion detectors generally have trouble getting good data above 20 data points per second, and classrooms aren't usually more than 2-3 meters high.  Even if you're dropping a full 3 m, that gives a fall time of only 0.77 s, and only about 15 data points for the detector.  Don't even talk to me about getting an object large enough and flat enough to reflect detector's sound waves consistently, but heavy enough such that air resistance can be ignored.

Oh.  But I found such an object.  Look at the picture. 

I stored a 15 pound medicine ball for a year in a cabinet.  One side flattened, as you see; and it doesn't unflatten easily.  Awesome.

So a student stood on a lab table holding a motion detector on the ceiling, pointed down.  A second student dropped the ball from 20 cm below the detector, with the flattened side pointing up.  I got the cleanest line on a velocity-time graph that I've ever gotten from a free fall experiment! I told the LabQuest to do a linear fit on just the straight segment, and voila... 10 m/s/s was the slope.