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16 November 2023

Directions of motion are "toward the detector" and "away from the detector".

A fundamental principle of teaching first year physics students is to never trust a student with a negative sign.  The linked post details ways that I avoid negative signs wherever possible.

My conceptual class never gets to the full-on kinematic equations - for them, all motion either is constant speed, using d = vt; or starts/ends at rest, making d = (1/2)at^2 or d = v^2/2a valid.  Since we never discuss computationally an object that changes direction of motion, we can dispense with the negative signs!

AP-level algebraic kinematics is one place where I haven't found a way to avoid a negative sign.  Yet!  Before we ever touch computation with kinematics equations, my AP class learns about position-time graphs, velocity-time graphs, and the definition of acceleration without any negative signs.  In fact, both classes begin with the exact same facts and exercises.  For position-time graphs, the facts are:

The steeper the position-time graph, the faster the object is moving.

A position-time slope like a front slash / means the object is moving away from the detector.

A position-time slope like a back slash \ means the object is moving toward the detector.

To determine how far from the detector an object is located, look at the vertical axis of the position-time graph.

After a number of in-class laboratory exercises with motion detectors, students are used to relating the way a position-time graph is sloped to whether a cart moves toward or away from a detector.  This takes about a day of class for AP, about three days of class for conceptual.  They're ready for the next step.

A daily quiz question eventually asks, "A motion detector points north.  The position-time graph it produces is sloped like /.  Which way is the object moving?"

When we grade this quiz together, I cite the fact: "A position-time graph sloped like a front slash means the object is moving away from the detector.  Count the question correct if the student wrote 'away from the detector,' or even just 'away.'"

But I go on. I call a student to the front of the room and hand them a motion detector.  "Please place this detector on the track and point it north."  I usually have to help the student figure out that "north" is different from "toward the ceiling."

Next  I call a different student up.  "Here is my pet hippopotamus Edna.  Please help her move along the track away from the detector."  The student does so.  "Which way was Edna moving, north or south?"  Now it's obvious that Edna was moving north.  "So, the best answer to this question is that the object moves north.  If a student wrote "north" as their answer, count it correct AND add one bonus point."

"From now on, if a question indicates the direction the motion detector is pointing, answers should no longer state just 'toward' or 'away from' the detector.  Your answers should be north, south, east, west, left, right, up, down, etc."  And I hold students to that.

The only difference for AP is, eventually they get to computational kinematics with changing direction of motion.  So we talk about defining directions as "positive" and "negative" so the math works out.  And we define that the direction "away from the detector" is the "positive" direction, by definition.

Interestingly, despite this roundabout and indirect way of introducing what "positive" and "negative" mean in the context of kinematics, my AP students don't generally have difficulty interpreting an exam question that does use negative signs to indicate direction!  They perform way above the national average on the exam, including on the unit 1 kinematics questions.  And those who do take calculus-based physics transition to using coordinate systems as if they were native Cartesians.