This is a series of applets drawn from the website mathMINDhabits [sites.google.com/site/mathmindhabits]. These applets are designed for teachers of physics who want to deepen their understanding of the physics they teach and that their students are expected to learn. Ideally, they will help teachers to better pose stimulating and engaging questions to their students.
In trying to understand the nature of motion we are confronted with the problem of reconciling two profoundly different representations of motion. One representation is the path (trajectory: f(x,y,z)=c ) taken by the object in motion as it moves in three dimensional space. The eye perceives that path and the brain "records" it.
Unfortunately, the representation of the path traversed is inadequate for understanding the motion - it does not tell us where the object was at any given time nor does it tell us how fast the object was moving at any given time. We need to complement the representation of the motion by a trajectory with images that supply the missing information, i.e. graphs of position and velocity as function(s) of time, i.e. [x(t), y(t), z(t), x'(t), y'(t), z'(t) ]. These images are not images that our eyes ever perceive - they are, however, needed images for the mind's eye.
Taken together, the images for the eye and the images for the mind's eye of physics address the question of "how does it move?" - they do not address the question of "why does it move?". This distinction between description and explanation is an important one and one that teachers would do well to get their students to think about.
Many of us have observed youngsters interpreting a rising line in a distance-time graph as "the girl climbed the hill" and a descending line on the same graph as "the girl came down the hill". College students often confuse the parabolic trajectory of a thrown football [an image for the eye] with the parabolic form of the graph of the football's height as a function of time [an image for the mind's eye]. The applets in this collection all deal with motion and are an attempt to help the user to become nimble is moving between images for the eye and images for the mind's eye.
