## The origin of a misconception

I felt like a made a tiny iota of a difference at school this Thursday–which was nice! The students were introduced to the concept of speed in a unit on motion and forces. After learning that speed = distance/time, they were shown a distance vs. time graph from their textbook to give them a graphical representation–such as this one:

What freaked me out is that the increasing and decreasing slope lines were described as “speeding up” (acceleration) and “slowing down” (deceleration). That is not accurate when describing this type of graph. Lines with a constant positive or negative slope on a distance vs. time graph are simply the movement of an object at a constant speed > zero. (I’m not even going to get into velocity here.) Horizontal lines show the object at rest. For an object to show acceleration (or deceleration) graphically, the line must be curved, like the blue one in the following diagram:

The only way a straight line can refer to acceleration/deceleration is if the graph is changed to VELOCITY vs. time:

Here, a line with a constant increasing or decreasing slope refers to acceleration, a flat line is a constant velocity (i.e. speed), and the point where the line crosses zero signifies an object at rest.

I reminded my teacher of this and we went through the other materials that she had been given (to help teach the concepts!). We found that most of them incorrectly noted acceleration of an object when it was supposed to be traveling at a constant speed. Eek! This was really disappointing to me because I remember how hard it was to understand graphical representations like this when I was a middle schooler, without being told the wrong thing. Hopefully my teacher and I were able to prevent the students from developing any misconceptions in graph interpretation…this time!