Summer School Physics —
Forces and Motion
Developed by the Cosmology
Research Group, UCB Physics Department, and Emery USD
PART I:
Three Lessons in Physics—Speed, Velocity, and Acceleration
Teacher's Guide
Objective:
 To effectively teach 8th graders the concepts of displacement, path,
speed, velocity, vectors, and acceleration.
 To do this with a handson approach emphasizing connections between
these concepts and students’ everyday lives.
Students Prerequisites:
 Basic math skills of adding, subtracting, multiplying, and division;
fractions
 Ready to be introduced to equations such as distance=time*speed
Estimated Time Requirement:
This module is written as an intensive three schoolday series. The lesson
for each day involves in the classroom and outside components,
which may be split up in the course of the day. Total time per day is estimated
to be three to four hours.
Day 1: Displacement,
Path, Speed
~in the classroom~
 Teacher hands out copies of a city map to each student. This city,
which will be familiar to the students, should be organized into a regular
grid pattern.
 The teacher asks students to mark down a route from point A to point
B on the map, say, from the market to the movie theater.
 The teacher asks students to calculate the distance from A to B in
their lab books, using the map’s distance scale. (Note that if the city
is truly in a grid pattern, then all groups will get approximately the
same distance.)
 Ask students to estimate how long it would take them to reach point
B on their skateboards/scooters or walking/running. Have them write
down these estimates in their lab books. They will conclude that the
time depends on the speed of their travel. At this point, the teacher
should lead a class discussion on speed that answers the questions:
 What is speed?
 How is it measured? (Units should be discussed here.)
 What is its relation with travel time and distance? (Namely,
derive the relation, RT = D.)
 Given this relation, how do we calculate speed from D and T?
 The teacher introduces the experiment below to the students and then
works out an example of how to find speed from elapsed travel time and
distance. The example should be worked out on the board, perhaps using
planes or train as the mode of travel.
~Outside~

Outside, students break up into groups of three to
perform the following experiment(s) {each group will need a tape
measure, a stopwatch, a TI with the speedometer device, some sidewalk
chalk, and a vehicle}:
Each group measures off a straight interval, say seven meters long,
and marks the endpoints with chalk. One member of each group stands
at each of these endpoints while the third person gets ready to travel
the course. The person at the opposite end of the course has a stopwatch
and gets ready. The traveler then speeds up to top speed before passing
the person at the beginning of the course. At this moment, the person
at the beginning of the course yells, “time!” and the person with
the stopwatch begins timing, only to stop when the traveler (who is
maintaining constant speed) reaches the finish line. The elapsed time,
interval length, and name of the traveler should be recorded. Students
may switch roles and conduct the experiment a few times to acquire
more data, or to compare different people’s maximum speeds. If time
permits, students can also explore the concept of instantaneous speed
using the TI speedometer device. This experiment uses the same setup
except, when the person at the start line yells, “time!” the person
at the finish line, who now has the TI, notes the time as the calculator
graphs speed versus time. This experiment will also emphasize the
fact that the previous experiment results in an average maximum speed.
An accurate drawing of this plot as well as the traveler’s name should
be recorded in each group member’s lab book.

In their lab books, students record their experimental
procedure and then their calculation of how long it will take to get
from A to B using the data.

For homework, students can be asked to write down
their ideas of the common speeds for a variety of objects, for example,
planes, snails, trains etc. These might be in the American or the
metric system, or both.
Day 2: Velocity
and Vectors
~in the classroom~

To motivate the concept of vectors, the teacher demonstrates
the independence of the x and y coordinates of a
point that travels through a simple path. When the class understands
this model, the teacher should add the position vector arrow and then,
again, allow the students to observe the independence of coordinates
as the point’s position vector moves along the path.
[If this demonstration cannot be set up using the program Fathom,
then time elapsed chalkboard drawings will be fine.]

The teacher observes from this demonstration that
to specify a vector, it is necessary to specify a magnitude
and a direction, and this can be done by giving coordinates.

The teacher has the students recall what they did
on the previous day by asking to hear some of their speed estimates
from the homework (or they can make up these estimates on the spot).
This should lead into a class discussion on how it is often necessary
to head in directions that are not straight to a final destination
in order to get there. The route paths the students marked out on
the previous day should be used as proof of this. Finally, the teacher
introduces the concept of the velocity vector as a way of keeping
track of speed and direction throughout the course of travel.

Students are then asked to use these route paths to
draw the velocity vectors at regular time intervals throughout their
hypothetical route. They should take into consideration obstacles
in their paths and the maximum speed they calculated the day before.
This will not be too difficult because there are only four possible
directions on a grid map, in which the velocity vector can point.

If they seem comfortable with the above, students
can be asked to do the same thing on a map with a curvy route and
velocity marked out at regular time intervals throughout the path.
This will, of course, be more difficult.
~Outside~

Students divide into groups of five to perform the
following experiment {each group will need a tape measure, three
stopwatches, some sidewalk chalk, and a vehicle}:
In each group, students created a connected path composed of three
straight segments of not necessarily equal length (but not too short).
One student shall stand on each of the four segmentation points of
the path. Each of the last three students on the path holds a stopwatch.
Just like before, a traveler speeds down the path. Each of the stationary
people yells, “time!” to the next stationary person as the traveler
passes his or her segmentation point. Note that it is not necessary
for the traveler to maintain a constant speed throughout the course.
This process will generate a travel time for each of the segments.
The students should record the travel times, segment lengths, and
an accurate drawing of the path in their notebooks.

With these measurements in hand, students will be
asked to fully describe the trajectory of their group’s traveler by
drawing the traveler’s velocity vector for each segment. [If time
permits, the groups could trade lab books and be asked to act out
the trajectory described in the other group’s lab books. This will
show, that the use of the velocity vector concept is necessary to
completely describe the path of a traveler].
Day 3: Acceleration
~in the classroom~

As a warmup, students are asked to think of possible
ways in which their journey from point A to point B is obstructed
or slowed down and then to list these obstacles in their lab books.

The teacher leads a class discussion on these delays,
which ends with the conclusion that the calculated travel time on
Day 1 needs to be revised to consider the fact that they must speed
up and slow down all throughout their transit.

The teacher explains the concept of acceleration as
being a change in speed or direction. (It may be too much to explain
how acceleration is also a vector quantity.) This might be facilitated
by drawing trajectories on the board (with velocity vectors) and asking
student to identify places where acceleration occurs. This will take
a while. Then, arguing by its analogy with R*T = D, the teacher
introduces the relation A*T = V and discusses with the class
how they might go about designing an experiment to find A.

Limiting all travel time delays to street intersections,
students will be asked to make a hypothetical graph of speed versus
path length throughout their travel from A to B. To make this graph,
start by marking all the points along the path length axis at which
0 velocity is expected (the intersections). Then mark the line speed
= max speed on the other axis. Then use these constraints to
draw a reasonable graph. This plot will concretely illustrate the
need to consider acceleration.
~Outside~

Student divide up into the groups of 6 and conduct
the following experiment {each group will need a tape measure,
a stopwatch, a TI with the speedometer device, some sidewalk chalk,
and a vehicle}:
The groups mark off a straight path divided into four fourmeter long
segments. One person stands at each of the segment line, including
the start line and the finish line; in total, five students standing
along a path at fourmeter intervals. Except for the person at the
start line, each of them holds a stopwatch. The sixth member of the
group, the traveler, gets ready at the starting line. When the person
standing next to the start of the path says “Go!” all the people with
stopwatches begin timing, and the traveler starts down the course.
Each time the traveler reaches the end of a segment, the timer for
that segment stops the watch and records the time traveled. When the
traveler reaches the end of the path, the timers have their specific
times written down. These times and the name of traveler are recorded
in each group member’s lab book. Students can then switch roles and
conduct the experiment again.

In their lab books, students calculate the average
speed for the traveler as determined from the starting point to the
end of each segment. These speeds should then be graphed in a histogram
with speed as the yaxis and displacement from beginning
of the course as the xaxis. The different speeds obtained
from each time will demonstrate that the traveler has accelerated.
Prepared by Miguel Daal 7/22/02
Part 2: Acceleration and Forces 