Kreutter: Kinematics 4
Lesson 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/web-pages/simulations-base.html and click on the simulation The Moving
Man. (You can get there from Mrs. Kreutter’s “Physics Links” page as well.)
You should see a screen like the one shown. There is a man at top of the simulation who can move 10 m
in either direction from the origin. The simulation also 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.
To eliminate the walls, click on “special features,” then click on “free range”.
Use your hypothesis (the mathematical model you created) from activity 4.1 to predict the man’s position
for the following scenarios:
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?
Adapted from PUM: Kinematics
©2010, Rutgers, The State University of New Jersey
Kreutter: 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.
4.3 Test Your Idea
Use your newly modified hypotheses from the previous activity to predict how you’d have to move so that
a motion detector creates position versus time graphs that match the graphs in the previous activities.
Explain how your prediction compares to the outcome.
4.4 Reason and Represent
In this activity you will be acting as the Moving Man or Woman. Below are a number of position vs. time
functions and written descriptions. Here you will have to act out how to move so that a motion detector
creates position versus time graphs match description provided. Before acting it out, discuss how your
motion should match the written and mathematical descriptions.
a) A person is 7.0 m away when we start observing and walks towards the origin at 0.4 m/s.
b) You are 5.0 m away from the origin at the initial clock reading and walk at 1m/s for 4 seconds
towards the origin stop for 3 seconds then walk 0.5 m/s for 6 seconds away from the origin.
c) x(t) = 5m +(– 0.7m/s)t
d) x(t) = 0.8m + (1.2m/s)t
Adapted from PUM: Kinematics
©2010, Rutgers, The State University of New Jersey
Kreutter: Kinematics 4
Homework
4.5 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.
4.6 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!
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.
Position
b) Write a function for the position as a function of time for the object’s motion.
6
4
2
0
-2 0
-4
-6
-8
-10
1
2
Clock Reading
4.7 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)
Adapted from PUM: Kinematics
©2010, Rutgers, The State University of New Jersey
3
4
5
Kreutter: Kinematics 4
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.
4.8 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?
4.9 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?
4.10 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).
4.11 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?
4.12 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?
4.13 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 grow 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? How you can report the result so it looks reasonable?
A little help…
Significant digits
When we measure a physical quantity, the instrument we use and the circumstances under which
we measure it determine how precisely we know the value of that quantity. Imagine that you wear a
pedometer and wish to determine the number of steps on average that you make per minute. You walk
for 26 min (as indicated by your cell phone) and see that the pedometer shows 2254 steps. You divide
Adapted from PUM: Kinematics
©2010, Rutgers, The State University of New Jersey
Kreutter: Kinematics 4
2254 by 26 using your calculator and it says 86.692307692307692. If you accept this number, it means
that you know the number of steps per minute to within 0.0000000000000001 steps/minute. If you accept
the number 86.69, it means that you know the number of steps to within 0.01 steps/minute. If you accept
the number 90, it means that you know the number of steps within 10 steps/minute. Which answer should
you use?
The number of the significant digits in the final answer should be the same as the number of
significant digits of the quantity used in the calculation that has the smallest number significant digits.
Thus, in our example, the average number of steps per minute should be 86, plus or minus 1
steps/minute: 86±1. In summary the precision of the value of a physical quantity is determined by one of
two cases. If the quantity is measured by an instrument, then its precision depends on the instrument
used to measure it. If the quantity is calculated from other measured quantities, then its precision
depends on the least precise instrument out of all instruments used to measure a quantity used in the
calculation.
Another issue with significant digits arises when a quantity is reported with no decimal points. For
example, how many significant digits does 6500 have—two or four? This is where the scientific notation
helps. Scientific notation means writing numbers in terms of their power of 10. Example: we can write
3
6500 as 6.5 x 10 . This means that the 6500 actually has two significant digits. If we write 6500 as 6.50 x
3
10 it means 6500 had three significant digits. Scientific notation provides a compact way of writing large
and small numbers and also allows us to indicate unambiguously the number of significant digits a
quantity has.
4.14 Evaluate On the web you might find the following statement: “The speed of hair growth is roughly
1.25 centimeters or 0.5 inches per month, being about 15 centimeters or 6 inches per year. With age the
speed of hair growth might slow down to as little as 0.25 cm or 0.1 inch a month.” Is this result consistent
with your estimate? Are the significant figures for different measurements consistent with each other?
Adapted from PUM: Kinematics
©2010, Rutgers, The State University of New Jersey