Return to Physics IndexStraight Line Motion with a Stomper

Ann 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 g

mass, 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 graphsand 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 willnotbe a

straight line this time. It should look like a parabola, because the speed is

increasing, the slope will increase. The velocity graphwillbe 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 tocompare 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 shapeof 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 slopesPerformance 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.