GOALS OF POSITION VS. TIME DEMO
Early on in introductory physics, students are exposed to position vs. time,
velocity vs. time, and acceleration vs. time graphs as they study simple
kinematics. It has been shown that some students are not very familiar with
graphs that are not x-y graphs, but are rather t-x graphs. Thus, they interpret,
in some cases, the slopes of an object moving in 1-D as indicating that the object
is actually following a sloped path in 2-D space. The confusion is compounded
by the use (at about the same time in the course) of trajectories, which ARE paths
in 2-D or 3-D space, but are also functions of time.
In order to get students comfortable with reading a t-x graph and using it to
understand a particle's velocity and acceleration, some sources recommend having
the students act out the motion of the particle, using the t-x data points as a
"motion script".
These videos illustrate this in my classroom at Tech. One student is shaking a can
with a bead in it, ticking the clock. Another student is reading position coordinates
from a list that is updated once/second (clock tick). The young woman is the particle,
trying to follow the script. In the first and second videos, she follows it well.
In the final video, the velocities are rather large and the particle reverses direction
several times. Entertainment was certainly a factor in the design of this final trajectory.
While it is not clear in the video, you see that an overhead projector is on. The
projector is showing the t-x graph that the student is acting out. The other students
are standing at front of class as points on the number line.
R.Sonnenfeld
New Mexico Tech Dept of Physics
2/20/2005