Open-ended lab exercise: is it constant acceleration?

The College Board has published a set of "Inquiry-Based Laboratory Investigations" for AP Physics 1 and 2.  The downside is that, in order to get to the actual investigations, you have to sort through page upon page of ed-school baloney about "learning objectives" and "building a community of learners" and "exemplifying technology-enhanced interfaces in data-driven schools."*  

* I might have made that last one up with the educational jargon generator.  But check the CB publication to be sure.

The UPside -- and it's a pretty important upside -- is that the investigations themselves include lots of excellent lab ideas from really good physics teachers.  Don't think of these "investigations" as lab guides which you must use verbatim.  Use them instead as a teacher-tested resource to give you good ideas, especially for more open-ended experiments in which students have to design their own procedures.

Now, I'm a big fan of such open-ended exercises, but I only use them in the latter half of the school year.  My students don't come to me with enough basic lab skills to dive straight into even "What factors do and don't affect the period of a pendulum?"  I spend the first part of the year riding herd about collecting lots of data across an entire parameter space, linearizing a graph, using the slope and intercept of a best-fit line to determine physically meaningful quantities, etc.  Once my students begin to see the laboratory process as a bit repetitive, then it's time to give them open-ended challenges.  A couple weeks ago I did "Does a rubber band obey Hooke's Law?"  I submitted this elaborate writeup for the College Board; but in class, I present just the question, and let the students take it from there.  By the time we do this experiment, the principle that they must make a graph and use its best-fit line is well ingrained such that it doesn't even need a discussion.

The very first investigation in the CB's Laboratory Investigations publication put a marble on a track, and asked the student to design and carry out a procedure to determine whether the marble's acceleration was or was not constant.  The experimental setup precluded simply using a motion detector to check for a linear velocity-time graph -- a standard motion detector can't read the marble.  So students have to use stopwatches and metersticks, or video analysis.  In either case, it's a non-trivial exercise requiring significant physics comprehension to explain how to translate from the raw data -- which only show position and time -- to instantaneous acceleration at several locations along the track.

I may come back to this particular exercise in my laboratory later this year.  But for now, I adapted the question as a Direct Measurement Video homework assignment.  This video shows a wind-up toy car speeding up across a table.  I simply ask, "How would you determine whether the toy bus's acceleration is constant? Answer in a clear, coherent, paragraph-length response."  

 I was glad I waited until last week to give this assignment, even though we covered kinematics long ago.  The class had a lively discussion the next day -- a discussion that wouldn't have happened so readily earlier in the year while the class was more answer-focused, while the class was less confident in the difference between acceleration and velocity.  Even those who got the problem wrong on the homework understood their mistakes.  We discussed how to estimate instantaneous velocities at different positions.  We discussed whose method of determining instantaneous velocity was best.  (Early in the year, the question would have been "but is mine right or not?"  Now we have enough experience to understand varying degrees of accuracy in an experimental situation.)  

I'll save the numerous methods of determining whether acceleration was constant for a future post -- feel free to share your idea in the comments.  Or, better yet, give this assignment to your class.  See how they do.  Whiteboard the student-generated results.*  Tell me and other readers your ideas for follow-up questions.  In other words, use the comments to talk shop.

* Sorry, jargon generator again.