Heresy: I don’t even mention the difference between speed and velocity

From John:

If a velocity is negative and the object is slowing down, do we say its velocity is decreasing since the magnitude is getting smaller, or do we say it is increasing since it is getting a higher value on the y-axis of a velocity/time graph?

Simplest answer: the question is not well posed.  Are we talking about the magnitude of the velocity vector, a.k.a. the speed?  Or are we talking the mathematical velocity function? The mathematical function is increasing; the speed is decreasing.

Better answer: This is a prime example why I avoid negative signs in first-year physics.  As soon as we talk about velocity as being positive or negative, we introduce an unnecessary abstraction that does nothing but impede comprehension.

Sure, you can try to resolve the conundrum by explicitly defining a positive direction, making a velocity-time graph, and explaining that while the velocity function increases, the absolute value of the function decreases, so the object slows down.  This is still too mathematical for first year students. Such folks do not have the intuitive understanding of functions that we physics teachers do. Don’t believe me? Give a quiz on which you ask them to define “magnitude” in their own words, without feeding them a canned textbook definition.  They will have no clue.

I know it is heresy of the highest order, and I will likely be stuck down by a bolt of lightning*.  But I recommend using the terms “speed” and “velocity” interchangeably, as synonyms. I try to say “speed” as a rule, but problem statements from external sources and students themselves use the word “velocity,” so I just translate to “speed.”

*Or a tornado… forty AP physics readers had to huddle in the lobby of the Crown Plaza last night as the local news blared with video of the apocalyptic storm which passed maybe a mile to our west.  Veteran AP readers have now lived through tornadoes in Nebraska, Colorado, and Missouri. Perhaps we could hold the reading in Vancouver?

Now there’s no conundrum!  In John’s case, the object is slowing down, so the speed is decreasing.  That’s, um, what “slowing down” means.

True, students have to work through some confusion on velocity-time graphs.  The fact sheet we use teaches students to memorize that speed is found by the vertical axis of a v-t graph; and the direction of motion is determined by whether the graph is above or below the horizontal axis. Above the axis represents motion “away from the detector,” while below the axis is motion “toward the detector.” (See, no use of the word “negative”!).  

The first time that someone organically encounters John’s graph, where (in mathematical language) the velocity function increases but speed decreases, some students are certainly confused.  Especially the mathematically astute folks want to tell me that the cart speeds up because the function increases, getting less negative. What do I do? I answer loudly, so the whole class hears, with one of the following lines of reasoning, both of which end in a wry smile:

* What’s the vertical axis value at the end of the cart’s motion?  (Zero.) How can a cart speed up to a stop?  :-)

* You are pulled over by a police officer, who writes you a ticket for going 100 mph.  In court you argue, “but your honor, I was traveling southbound, which is the negative direction… so my velocity was negative 100 mph.  That’s significantly less than the posted limit of +65 mph.” Good luck. :-)

How, then, would a student explain such a graph? Ideally, they’d say “The vertical axis values are getting closer to zero, so the cart’s speed is getting closer to zero.  That’s slowing down. Since the graph is below the horizontal axis, the cart is moving toward the detector.”

I know this method will be pooh-poohed by many physics teachers, especially those who spend two full lab periods trying to teach the rigorous mathematical difference between speed and velocity.  You don’t have to teach my way. Yet, please look at the results. My conceptual freshmen can interpret the physical meaning behind motion graphs - by year’s end, they can do AP-level motion graph problems.  In AP, I do mention months later that “velocity” means include direction, while “speed” means do not. My AP students average above 4 on the exam… so I’m not hurting their comprehension.

Point is, try it.  Eliminate technical mathematical terminology from your physics class wherever you can.  Speed and velocity is a great place to start.

And if you read “Physics Teacher Hospitalized with Lightning Burns” as a headline in the Kansas City Star, you’ll know what I did to bring on such divine wrath.