Sierzega: Kinematics 4
The Moving Man
4.1 Hypothesize
An object is moving in the positive direction at constant velocity v. It starts at clock reading t = 0 sec, at a
position x0. How would you write a function that will allow you to find the position of the object at any time?
4.2 Test Your Idea with Phet Simulations
Go to http://phet.colorado.edu/ and type “the moving man” into
the search window and click Search. Click The Moving Man
hyperlink under Simulations, then click on the blue Download
box.
When the simulation window opens, click on the Charts tab.
The simulation includes axes of position, velocity and
acceleration graphs that will reflect his motion. Since you are
not going to use the acceleration or velocity graph right away,
you can close them by clicking on the small window in the
upper right hand corner of each section.
Use the hypothesized mathematical model in activity 4.1 to predict the position.
Scenario 1: The man’s initial position is 9 m and he is jogging to the left at 2 m/s.
a) Write an expression for the man’s position as a function of time.
b) Create a position vs. time graph for this function.
c) Before you continue with the simulation, check for consistencies between the written description,
function and graph for the man. How do you know they are consistent?
d) Predict the time when he passes through the position at 0m.
e) Perform the experiment by entering given quantities in the respective simulation boxes and click Go!
Compare your predicted value to the outcome of the testing experiment. Do they agree or disagree? If
they disagree, revise your mathematical model of the moving man’s motion.
Scenario 2: The man is walking at the speed of 0.75 m/s towards his home. When we start observing him, he is
at the position of 7 m to the left of the origin.
a) Write an expression for the man’s position as a function of time.
b) Create a position vs. time graph for this function.
c) Before you continue with the simulation, check for consistencies between the written description,
function and graph for the man. How do you know they are consistent?
Lesson activity adapted from ALG and PUM, Etkina and Van Heuvelen, 2010
Sierzega: Kinematics 4
d) Predict the time when he arrives at the house.
e) Perform the experiment through the simulation. Compare your predicted value to the outcome of the
testing experiment. Do they agree or disagree? If they disagree, revise your mathematical model of the
moving man’s motion.
Scenario 3: When we start observing the man is at the 5 m mark by the house and is running at the speed of 4.5
m/s towards the tree.
a) Write an expression for the man’s position as a function of time.
b) Create a position vs. time graph for this function.
c) Before you continue with the simulation, check for consistencies between the written description,
function and graph for the man. How do you know they are consistent?
d) Predict the time when he has traveled 70 m beyond the tree.
e) Perform the experiment through the simulation. Compare your predicted value to the outcome of the
testing experiment. Do they agree or disagree? If they disagree, revise your mathematical model of the
moving man’s motion.
Homework
4.3 Represent and reason
-10.0 m
∙ ∙ ∙ ∙ ∙
-5.0 m
0.0 m
+5.0 m
+10.0 m
Examine the dot diagram above. When we start observing the object it is at +7.5 m and moves in the negative
direction of the x-axis.
a) Describe the motion in words.
b) Sketch a position vs. clock reading graph.
c) Write a function for the position as a function of time for the object’s motion.
Lesson activity adapted from ALG and PUM, Etkina and Van Heuvelen, 2010
Sierzega: Kinematics 4
4.4 Represent and Reason
Thus far, you have represented the motion of a ball with different representations: dot diagrams, words,
pictures, tables, and now a graph. Explain how the different representations describe the same motion.
a) Use the graph below to describe the motion in words. Pay attention to what happened at zero clock
reading!
b) Write a function for the position as a function of time for the object’s motion.
c) You should notice that the two
physical quantities on the graph do
not have units. Describe a real life
situation for this motion if the units
were kilometers and seconds.
Describe another situation if the
units were centimeters and minutes.
d) Draw a picture for each of the
situations you described in part c.
4.5 Equation Jeopardy
Three situations involving constant velocity are described mathematically below.
1. (86 m)  v(1.72 s)  (100 m)
2. x  (5.7 m/s)(300 s)  (1000 m)
3. (120.0 m)  (5.7 m/s)(6.8 s)  xinitial
a) Write a story or a word problem for which the equation is a solution. There is more than one possible
problem for each situation.
b) Sketch a situation that the mathematical representation might describe.
c) Determine the unknown physical quantity.
4.6 Practice You are learning to drive. To pass the test you need to be able to convert between different
speedometer readings. The speedometer says 65 mph.
(a) Use as many different units as possible to represent the speed of the car.
(b) If the speedometer says 100 km/h, what is the car’s speed in mph?
Lesson activity adapted from ALG and PUM, Etkina and Van Heuvelen, 2010
Sierzega: Kinematics 4
4.7 Practice The speed limit on the roads in Russia is 75 km/h. How does this compare to the speed limit on
some US roads of 55 mph?
4.8 Practice Convert the following record speeds so that they are in mph, km/h, and m/s.
(a) Australian dragonfly—36 mph;
(b) the diving Peregrine falcon—349 km/h; and
(c) the Lockheed SR-71 jet aircraft—980 m/s (about three times the speed of sound).
4.9 Reason You are moving on a bicycle trying to maintain a constant pace. You cover 23 miles in 2 hours.
What is your speed in m/s? If you only rode half of the distance maintaining the same pace what would the
speed be? If you rode 43 miles, what would the speed be?
4.10 Reason James and Tara argue about speed. James says that the speed is proportional to the distance and
inversely proportional to the time during which the distance was covered. Tara says that the speed does not
depend on the time or distance. Why would each say what they did? Do you agree with James? Do you agree
with Tara? How can you modify their statements so that you could agree with both of them?
4.11 Hair growth speed Physicists often do what is called “order of magnitude estimations”. Such estimations
are approximate calculations of some quantity that they are interested in. For example, how do we estimate the
rate that your hair grows in mm/s? Think of the following: How often do you get haircuts? How long does your
hair grows during this time? Then convert the time between hair cuts to seconds and the length of your hair
growth to millimeters – then you are almost done. The question is – how will you report your results? What if
after dividing length by time you get a number on your calculator that looks like 0.005673489? Think how you
can report the result so it looks reasonable.
Lesson activity adapted from ALG and PUM, Etkina and Van Heuvelen, 2010