Name: ____________________________
Date:______________
Group Members: ___________________________________________________
1.2- Graphing Motion
Big Idea: Objects that move in translational motion are described in terms of position,
velocity, and acceleration.
Nature of Science Big Idea: In order to give meaning to their data, scientists and engineers
organize and interpret it through tabulating, graphing, and statistical analysis. Mathematics and
computation tools are essential to science and engineering.
Essential Question: How can the motion of an object be described in a measurable and
quantitative way?
Nature of Science Essential Question: In what ways are data analyzed and interpreted?
How are the tools of mathematics utilized in doing science? What are the benefits of
mathematics for science?
Goals for This Activity: Observe objects moving at a constant speed and objects moving with
changing speed.
 Graph the relationships between distance and time for moving objects.
 Interpret graphs relating distance and time for moving objects.
WHAT DO YOU THINK?
Why are graphs such a useful tool for interpreting data? ___________________________
________________________________________________________________________
MATERIALS
battery-operated toy car
meter stick
stopwatch
block, book, or clay
graph paper
track wooden block
masking tape
metal ball
The goal of the first part of this lab is to find out what a position vs. time graph of a
car moving at a constant speed will look like. To do this you will measure the distance
a battery powered car will travel in one second increments. You will then graph the
data collected and learn how to interpret the graph.
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PROCEDURE
Part 1:
1. Moving at a constant speed
a. Find a clear, flat surface a few meters long to perform your experiment.
b. Make sure the area is free of obstacles and traffic.
c. In order to ensure the car is up to top speed start the car moving about 0.25
meters before the spot you start timing.
d. Place a pieces of tape where your partner will start timing, on the tape write
“Time= 0 seconds and Distance = 0.00 meters”.
2. Start the car, observe the car as it moves. Be sure to start the stopwatch as the car crosses the
0.00 meters mark.
3. After 10.0 s, mark the position of the car with the masking tape.
Label this mark “10.0 s.”
4. Repeat steps 2 and 3 for 9.0 s, 8.0 s, 7.0 s, 6.0 s, 5.0 s, 4.0 s, 3.0 s,
and 2.0 s.
5. After you have marked with tape how far the car traveled each
second use the meter stick to measure the exact distance from the
0.00 m mark to each piece of tape. Remember to use meters for
your unit of distance not inches!!!
6. For each position marked with tape, record the distance traveled
Distance
Traveled
0 meters
Time
0 seconds
1 second
2 seconds
3 seconds
4 seconds
5 seconds
6 seconds
7 seconds
8 seconds
9 seconds
10 seconds
and time in the table below.
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7. As a class and with the teachers help you will learn how to create a graph with data collected from
the constant motion car.
a. With the distance on the “Y” axis and time on the “X” axis we need to come
up with an appropriate range of for each axis, as well as how far apart to
space the numbers.
b.
c.
d.
e.
f.
Now we need to label each axis including the proper units.
For this graph we will not have a legend.
Now it is time to place our data points on the graph.
Should there be a point at the origin?
After all data points are on the graph make a best fit line.
3
Analysis (Work through this with teacher.)
A. This graph displays the relationship between what two variables? _________
and ____________________
B. What are the units for distance and time? _______________ and ___________
C. How do you find the slope of a line? _________________________________
______________________________________________________________
D. How do you find the unit for the slope?
______________________________________________________________
E. What is the unit for the slope of your distance time graph?
______________________________________________________________
F. What information does the slope of a distance vs. time graph give?
______________________________________________________________
The equation for a line, slope intercept form, is:
y=mx+b
where “y” is what is being measured on the “y” axis, “m” is the slope of
the line, “x” is what is being measured on the “x” axis and “b” is where
the line intersects the “y” axis. Don’t worry too much about “b” for now
and mx means the value of m is multiplies by the value of x.
G. For our distance time graph what does:
y= _________
m=_________
x=__________
b=__________
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H. So, the equation for our graph is ____________________________________
I. Why is it helpful to create an equation for a graph? ______________________
______________________________________________________________
J. Using our equation we created from the graph how far would the car travel in
15 seconds?
Step 1, write down the equation: ____________________
Step 2, what does time equal _______________________
what does slope (m) equal ____________________
the y intercept is zero
Step 3, plug the numbers into the equation_____________
Step 4, solve for distance ___________________________
K. Repeat the previous steps to find the distance the car travels after 22 seconds.
 equation ______________
 time = _______________
 slope (m) = ___________
 plug in numbers _________________
 distance = ___________ (don’t forget units)
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Competition Time!!!!
Now we are going to have a little graphing competition. Below you see four
position vs. time graphs of a person walking. Your goal is to analyze these graphs and
figure out how the person is walking at each location: the person is at rest, moving fast
or slow, away from the origin or towards the origin. Then YOU become the person
walking. You and your partners have to walk the graphs as accurately as possible. A
score will be calculated for each graph. Whichever group ends up with the highest
score wins!
Now you will be split up in to groups of four. Each group member will have one graph
to walk, all members must walk. Before you and your group members walk the graph
you will first need to write down exactly how you plan to walk in order to match the
graph. Answer the following questions below ALL the graphs before begin.
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I.
For part “A” the person is at rest; how does the graph show this. Hint: do not
say, “Because the line is straight”. _________________________________
II.
For part “B” how do we know the person is moving? __________________
III.
Describe the motion of the person at “C”. ___________________________
IV.
Explain, using the graph, how you know this is the persons motion at “C”. ____
______________________________________________________________
______________________________________________________________
V.
What does the slope of any of the lines indicate? ________________________
As we already know the slope of a position vs. time graph gives velocity.
Also we know that to calculate slope we use the equation:
Slope =
VI.
∆𝒀
∆𝑿
=
∆𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏
∆𝑻𝒊𝒎𝒆
= Velocity
Calculate the velocity at of part “B”, Show all your work.
VII.
The slope of the line is positive, meaning positive velocity. How does the graph
indicate the velocity is positive? _____________________________________
VIII.
What would the slope look like if the velocity was negative? _______________
______________________________________________________________
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I.
Describe how the person is moving for all the different parts of the graph.
Remember to include if the person is moving towards the origin or away.
i.
ii.
iii.
iv.
v.
II.
A: ________________________________________
B: ________________________________________
C: ________________________________________
D: ________________________________________
E: ________________________________________
Calculate the velocity of part “B” and “D”. Then give a written explanation
comparing the two, remember to write in complete sentences and to explain not
just give an answer!
Calculation of velocity at “B”
Calculation of velocity at “D”
Explanation: ___________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
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I.
Describe how the person is moving for all the different parts of the graph.
Remember to include if the person is moving towards the origin or away.
i.
ii.
iii.
iv.
v.
II.
A: ________________________________________
B: ________________________________________
C: ________________________________________
D: ________________________________________
E: ________________________________________
Calculate the velocity of part “B” and “D”. Then give a written explanation
comparing the two, remember to write in complete sentences and to explain not
just give an answer!
Calculation of velocity at “B”
Calculation of velocity at “D” (remember direction here)
Explanation: ___________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
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II.
Describe how the person is moving for all the different parts of the graph.
Remember to include if the person is moving towards the origin or away.
i.
ii.
iii.
iv.
v.
A: ________________________________________
B: ________________________________________
C: ________________________________________
D: ________________________________________
E: ________________________________________
Group Name Graph 1 Graph 2
Graph3
Graph4
Total
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Unit I Reading – Graphical Methods
One of the most effective tools for the visual evaluation of data is a graph. The
investigator is usually interested in a quantitative graph that shows the relationship
between two variables in the form of a curve.
For the relationship y = f(x), x is the independent variable and y is the dependent variable.
The rectangular coordinate system is convenient for graphing data, with the values of
the dependent variable y being plotted along the vertical axis and the values of the
independent variable x plotted along the horizontal axis.
Positive values of the dependent variable are traditionally plotted above the origin and
positive values of the independent variables to the right of the origin. This convention
is not always adhered to in physics, and thus the positive direction along the axes will
be indicated by the direction the arrow heads point.
The choice of dependent and independent variables is determined by the experimental
approach or the character of the data. Generally, the independent variable is the one
over which the experimenter has complete control; the dependent variable is the one that
responds to changes in the independent variable. An example of this choice might be as
follows. In an experiment where a given amount of gas expands when heated at a
constant pressure, the relationship between these variables, V and T, may be
graphically represented as follows:
T
V
T
Correct
V
Incorrect
By established convention it is proper to plot V = f (T) rather than T = f (V), since the
experimenter can directly control the temperature of the gas, but the volume can only
be changed by changing the temperature.
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Curve Fitting
When checking a law or determining a functional relationship, there is good reason to
believe that a uniform curve or straight line will result. The process of matching an
equation to a curve is called curve fitting. The desired empirical formula, assuming
good data, can usually be determined by inspection. There are other mathematical
methods of curve fitting, however they are very complex and will not be considered
here. Curve fitting by inspection requires an assumption that the curve represents a
linear or simple power function.
If data plotted on rectangular coordinates yields a straight line, the function y = f(x) is
said to be linear and the line on the graph could be represented algebraically by the
slope-intercept form:
y = mx + b,
where m is the slope and b is y-intercept.
Consider the following graph of velocity vs. time:
10
vel
(m/s) 5
0
5
time (s)
1
0
The curve is a straight line, indicating that v = f(t) is a linear relationship. Therefore,
v = mt + b,
∆v v2 - v1
where slope = m = ∆t = t - t
2 1
From the graph,
8.0 m/s
m = 10.0 s = 0.80 m/s2 .
The curve intercepts the v-axis at v = 2.0 m/s. This indicates that the velocity was 2.0
m/s when the first measurement was taken; that is, when t = 0. Thus, b = v0 = 2.0
m/s.
The general equation, v = mt + b, can then be rewritten as
v = (0.80 m/s2 )t + 2.0 m/s.
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