VELOCITY LESSON PLAN
Part 1, “Wet” lab.
Simple Motion
In this activity we will concentrate on the simplest motion possible and make careful
observations. These observations, and the discussions, which follow, will lead you to a scientific
definition for the simple motion.
We will use some of the following equipment for this activity.
 Meter stick
Stop watch
 Tape measure
Heavy ball (such as a bowling ball)
 Graph paper
Ruler
Bean bags
We will start by looking at a class of simple motions. When faced with a phenomenon that is
new to them, scientists first consider the simplest case they can think of, before trying to describe
something extremely complicated.
Most people would agree that one of the simplest possible motions is when an object moves in a
straight line without speeding up or slowing down. We might call this a uniformly moving object
or an object that moves with a constant speed. We will now attempt to describe precisely what it
means to move with constant speed.
Activity: Measurements and Graphs
a) For our first experience with measurements and graphing, we will be measuring the distance
traveled by a rolling ball at specific instants of time. Please put the distance into meters.
Let’s work together to measure the distances traveled by a rolling ball at 1 second intervals.
Let’s try rolling the ball slowly the first time and then rolling the ball more quickly.
i) Briefly describe how we conducted this experiment.
ii) Record the data.
b) When scientists make graphs, it is customary to plot the independent variable along the x-axis
and the dependent variable along the y-axis.
What is an independent variable?
What is the independent variable for this experiment?
What is a dependent variable?
What is the dependent variable for this experiment?
Follow the directions given in class to graph this data on graph paper.
c) Most likely, your points will have some pattern, but will be a little bit scattered about this
pattern. Where do you think this scatter comes from? How might you reduce this scatter?
Do you think it is possible to eliminate this scatter completely? Explain.
d) Scientists are in the business of looking for patterns and simple relationships. Thus, when you
see a pattern like the one on the graph you just made, a scientist will often draw a “curve” through
the points. This curve represents a mathematical model of what the results of a “perfect”
experiment might look like, but will not touch all the points. In this case, your points should lie
approximately on a straight line, so the “curve” you draw will be a straight line. Remember, you
should not just try and connect the points (no dot-to-dot), but instead, try and draw the “best fit”
line that you can between the points. Explain your rationale for determining what the “best
fit” is (for those of you who have used r2, remember, close to 1.00 is best).
So, assuming that the small amount of deviation we see with the connecting the points is due to
human and experimental error, we would then assume that the overall pattern is a straight line –
and it is.
e) Find the slope (rise/run) and y-intercept of your best-fit line and record in your lab
notebook.
f) I feel that it is important that you make your first graphs by hand so that you know how a graph
is put together and how to calculate slope, etc. However, for most of the experiments this
semester we will use Excel to graph our data. Make a graph this data using Excel, add the
trendline and the equation to the graph and turn in a copy of this graph with your carbons.
If you don’t remember how to graph in Excel, the appendix “Graphing Help” may be useful.
Using the Motion Detector to Study Motion
In the last section you were introduced to graphical representation and mathematical
models. In this section we will introduce you to some of the powerful capabilities of
today’s personal computers by interfacing some electronic tools that will help simplify
the measurement process.
Tracking Motion with a Motion Sensor
We will be studying the motion of an object using a computer-based laboratory system
consisting of a microcomputer, an electronic interface, a sensor, and special software that
will help make the output of the electronic interface understandable by humans. One of
the sensors we will be learning to use is an ultrasonic motion detector. When the motion
sensor is attached to the computer, the distance of an object from the sensor is recorded
automatically. Computer software allows you to display these distances almost instantly
in the form of a graph. If the distance changes, you will see the graph of the object’s
position change instantly. In addition, the software can use a programmed set of rules to
calculate two other quantities that are used to describe motion from distance and time
measurements. These include velocity and acceleration. We will have more to say about
this in the activities to come.
Things to remember when using a motion sensor:
1. Do not get closer than 0.5 meters from the sensor because it cannot record reflected
pulses which come back too soon after they are sent.
2. The ultrasonic waves come out in a cone of about 15. They will “see” the closest
object. Be sure there is a clear path between the object whose motion you want to
track and the motion sensor.
3. The motion sensor is very sensitive and will detect slight motions. You can try to
glide smoothly along the floor, but don’t be surprised to see bumps representing your
steps in velocity graphs and even larger bumps in acceleration graphs. Try to
mentally level out these bumps and focus on the overall big picture.
4. Some objects like bulky sweaters absorb the signal and may not be “seen” very well
by a motion sensor. You may want to hold a book in front of you.
To do the activities that follow you should make sure that (a) an interface is plugged into
a power source and connected to your computer, (2) the motion sensor is plugged into the
interface and (3) that motion software has been located into the memory of your
computer. You should then set up the software to record Position vs. Time graphs for
about 15 seconds. Your instructor will give you other information that may be useful
In order to be able to use the motion sensor to get some useful data, you must first learn
how to use it. The next activity allows you some time to get familiar with the equipment
you will be using. You may need to ask your instructor for details on how your motions
sensor and software work.
Activity: Playing Around
a) To get a feel for the capabilities of the motion sensor, begin by simply standing in
front of it. Try walking slowly towards or away from the sensor. Are these
measurements similar to or different from the measurements you made with the
rolling ball?
b) One of the nice aspects of computers that they can do things extremely fast and
accurately. Walk with a constant speed towards the sensor. Now walk twice as fast
toward the sensor. Try walking away from the sensor. How do these graphs differ?
How do they compare with the predictions you made in PRELAB QUESTION
#3? Make a careful sketch of these graphs in your lab notebokk (mentally
smoothing bumps). Be sure to indicate units and label axes. Have your
instructor check your sketches. NOTE: the most important features are if the slope
is greater vs. less, + vs. - etc. Therefore, these aspects of the graph must be
preserved.
c) Look at the following position-time graph. Explain in your lab notebook what you
would need to do (in words) to reproduce this graph. Then try and reproduce it.
Check your reasoning for a) through c) with a staff member.
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3
Position (m)
2
1
0
0
2
4
6
8
10
12
Time (s)
So far we have been dealing with “uniform”, or constant velocity motion. When an
object moves with a constant velocity, we have seen that the position of the object
changes linearly with time, with the slope of the line representing how much the object’s
position changes in one second. This became our definition for velocity, at least for the
case of uniform motion. We have not yet considered what happens if the object is
speeding up or slowing down. What would a position vs. time graph look like then? How
can we define velocity? What would a velocity vs. time graph look like? These are some
of the questions that we will attempt to answer in the following activities.
Activity: The velocity-time graph
a) Notice that the computer software allows you to display two graphs at the same time.
Choose two graphs, and let one be a position graph, while the second is a velocity graph.
Now walk slowly away from the detector (constant speed), and make careful sketches of
the two graphs in your lab notebook.
b) Try walking slowly toward the detector (Constant speed). Again, make careful
sketches of the position vs time graph and the velocity versus time graph in your
notebook.
c) In your own words, describe how a velocity graph is related to a position graph.
Check these against your predictions in pre-lab question #4. Check your results with
your instructor.
Activity: Non-Uniform Motion—Experiments
a) Set up the motion detector so that the software is displaying both a position-time
graph and a velocity-time graph. Experiment with the following motions in front of
the sensor that are not uniform. To simulate speeding up in a car, try starting from
rest and then walking towards (or away from) the motion sensor, getting faster and
faster as time goes on. Try and obtain a velocity graph that looks linear. (It’s not as
easy as it sounds) Show a rough sketch of what you a) position-time and b)
velocity-time graphs look like in your notebook (mentally smoothing any spiky
areas). The compare to PRELAB question #5 and #6.
b) Repeat, but this time try walking toward or away from the detector while slowing
down. Again, sketch your two graphs in your notebook. Compare to PRELAB
question #7.
c) Set up the motion sensor to track the motion of a fan cart. Start the cart at rest, near
the motion sensor (at least 0.5 meters away) and let it accelerate away. Describe the
velocity-time graph and the position-time graph. Make careful sketches of the
two graphs in your notebook. Recall that our definition for velocity (for an object
moving with constant speed) had a nice graphical representation. The velocity was
equal to the slope of the position-time graph. Can you think of a way of defining
velocity when the position-time graph is not a straight line, as is the case with the
graphs above? That is, how would you define velocity when the velocity is not
constant?
d) What about acceleration? Since velocity describes changes in position and
acceleration describes changes in velocity, can you define acceleration similar to the
way velocity was defined? Give a definition for acceleration when the object’s
velocity is changing at a constant rate (this can be graphical or mathematical).
PART II. Simulation.
Go to the Moving Man applet by following the “Velocity” link at the bottom of the lesson
plan repository
(http://www.colorado.edu/physics/phet/simulations/movingman/movingman.jnlp).
Several of the above activities can be practiced and reinforced using “Moving Man”
applet. Then we will compare the results below to the results above.
1. Click on the man, and the clock will start. Move the man slowly to the right for
about 10 seconds. Try to keep the same speed. Is the velocity positive or
negative? ________Is it constant? ___________If you velocity is constant, what
is the acceleration?___________
2. Move the man with a constant speed to the left for about 10 seconds. What is the
velocity?_________ What is the acceleration?____________
3. Sketch the graphs you made in 1 and 2 above.
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4. Restart. Move the man very slowly to the right and increase its speed very slowly.
What is his acceleration?__________ Decrease his speed. What is the sign of his
velocity (+ or -)?_____ What is happening to his velocity? + (increasing) or –
(decreasing).___. What is his acceleration?
5. Draw a sketch of the graph you made in 4 above.
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6. KEY! Is it possible to have a positive velocity and a negative acceleration?
Explain.
7. Start the simulation over. Move the man to the left, increasing speed as you go.
a. What is the velocity?
b. Is he moving faster or slower?
c. Is acceleration positive or negative?
8. So. Can you have a negative acceleration but be speeding up? Explain.
9. Practice moving the man by moving the arrows along the right side for position,
acceleration, and velocity.
10. Which is easier to control (for instance, move at a constant speed? Move to a
selected location. Move with a specific acceleration?)? Moving the man by
clicking on the man or with the sliders? Explain.
11. Now that you can control the moving man, see if you can create a distance vs.
time graph like in PART 1, Playing Around, C) on the top of page 4. Describe
how you created that graph using the moving man.
12. Compare the Moving Man activities 1-11 to the wet lab activities. How were they
alike? How were they different? What did you understand better after doing the Moving
Man?