```Straight Line Motion with a StomperAnn Brandon                    Joliet West High School                               401 North Larkin Ave                               Joliet IL 60435                               (815) 727-6950Objectives:After this experience, the student should   1.  be able to define average speed (distance traveled/time)   2.  be able to graph distance vs time and velocity vs time   3.  be able to find the velocity from the distance time graph (slope)   4.  be able to find the acceleration from the velocity time graph (slope)   5.  recognize constant velocity, constant acceleration and changing        acceleration from the shape of the distance-time and velocity-time graphsMaterials needed:   (for each group)Stopwatch, meter stick, Stomper (battery powered toy car), large washer or 100 gmass, tape, paper tape (ticker tape) and a recording (ticker tape) timer, Tricycle (optional).Strategy:     Part I:  Begin with the Stomper.  Show it going in a straight line along the counter top.  Ask:  How fast is it going?  What do we need to know to find out?  (You need a distance traveled and a time.)  Give each group a Stomper, stopwatch and meter stick.  They should determine the average speed of their Stomper.  It should take 10 or 15 minutes for them to do several trials.      Part II:  How fast was the Stomper going as it moved along?  Was it going the same speed everywhere or did it speed up or slow down?  Point out:  The stopwatch is only good for substantial times, several seconds.  It will not help us answer this question.  Demonstrate the recording timer by pulling a meter or so of tape through it.  Explain why the time intervals are equal and ask why the spaces are not even.  (The spaces are small where the speed was small.)      Each group should do two runs with the Stomper pulling a length of ticker tape behind it.  Mark off each tape in groups of six dots.  (Each six is one tenth of a second.)  The first tape will become a distance-time graph.  Rip each six dot section and glue it to a piece of graph paper.  The first section goes on next to the origin.  The second section goes over one width of tape, but starts up, so that its bottom is next to the first tapes' top.  The third goes over one and its bottom lines up with the top of the second section, etc.  Thus the vertical axis is the distance traveled in cm. and the horizontal axis is the time in tenths of a second.  This graph will have a constant slope equal to the average speed found with the stopwatch.  Demonstrate how to find slope.      The second tape will become a velocity-time graph.  Each six dot section is the distance traveled per tenth of a second, so it is the average velocity for that tenth of a second.  For this graph the vertical axis is the velocity in cm per tenth of a second, while the horizontal axis is again the time in tenths of a second.  For this graph, each tape has its bottom on the horizontal axis.  The tapes go next to each other in order.  This graph will have a slope very close to zero because the speed is very close to being constant.  How did this velocity compare to the slope of the first graph?  How did it compare to the speed found with the stopwatch?      Be certain that you ask the students to describe each of these two graphs
and to compare them to each other.

This is probably as much as you can expect for one day.  I would then spend
a day or so doing constant velocity problems to reinforce this concept.

Part III:  Constant Acceleration     Drop a mass.  (Catch it!)  Ask if this is constant velocity.  Ask how you can find out.  Using the recording timers, attach the tape to the mass and drop the mass over the side of the table.  (It pays to protect the floor with a book, or a newspaper.)  Run two tapes.  Mark every sixth dot and create a distance-time and a velocity-time graph.  Look at them!  The distance graph will not be a straight line this time.  It should look like a parabola, because the speed is increasing, the slope will increase.  The velocity graph will be a straight line, but will not be horizontal, because the speed is increasing at a constant rate. The slope of this line is the acceleration.  (The change in velocity/the time it took (dV/dt).)      Again, it is very important to ask what these graphs look like and to
compare them to each other and to the graphs from Part II.

This is probably a second day's work.  It should be followed by problems
with distance, velocity and constant acceleration.

Part IV:  Constantly Increasing Acceleration     Lay a chain on the counter top.  Push it over the edge one link at a time, until it goes by itself.  Ask what kind of motion this is.  Again, we can analyze this motion if we attach a tape to it.  Mark every sixth dot.  The distance time graph is optional, be sure to do a velocity time graph.  This will not be a straight line because the velocity increases at an increasing rate.(The acceleration (slope) increases at a constant rate, thus we get a parabola.)      It is once more imperative that you ask the students to describe the shape
of the graph(s) and compare them to the previous graphs.

Optional:  Have Tricycle races.  Have someone ride a tricycle pulling ticker
tape.  The velocity-time graph is the most interesting.  Be sure to ask about
the accelerations.  They will be positive and negative!

Conclusions:  Velocity is the distance traveled/time it took (dD/dt)  Velocity is the slope of a distance-time graph  Acceleration is the change in velocity/time it took (dV/dt)  Acceleration is the slope of a velocity-time graph  Constant velocity gives straight line graphs for both d-t and v-t  Constant acceleration gives parabolas for d-t, but straight lines for v-t  Changing acceleration gives v-t graphs with changing slopes Performance Assessment:    Using TWO SPEED Racer (a friction car, about \$2.75 at "Toys R Us"): Show it to the students.  Placing it on a flat surface, where all of them can watch it, pull it back until you hear a click.  Let it go.  It will go in a straight line, and suddenly increase its speed.    Ask the students to sketch two graphs.  A Distance vs Time and a Velocity vs Time graph.Rubric:5 pts  Graphs are correctly labeled on each axis. Distance-time graph shows as        short straight line, sloping up followed by a steeper straight line; also        sloping up.       Velocity-time graph shows a short, horizontal line, followed by a higher        horizontal line.4 pts  Graphs not correctly labeled, but show the proper shapes.3 pts  Graphs not correctly labeled, and only one of the graphs shows the proper        shape.2 pts  Graphs properly labeled, but neither graph is the proper shape.0 pt   No labels, and wrong shapes.Multicultural Applications:    There are many applications of distance vs time in life including the Summer Olympics track competitions and the speed skating and cross country skiing in the Winter Olympics.```