INVESTIGATION
B2
B2 Speed, Acceleration, and Free Fall
Key Question: How does gravity affect the motion of a falling object?
Earth’s gravity pulls objects downward toward the center
of Earth. In Investigation B1, students learned to measure
the speed of a falling marble. In this investigation,
students apply their knowledge to examine the speed
of the marble at several points along its path. With this
information, they determine how the speed of the falling
marble changes as it falls. Students then learn to graph
their results, find slope values, and create a mathematical
model to confirm their measurements.
Learning Goals
✔✔Make a graph of the motion of a falling marble.
✔✔Interpret motion graphs.
✔✔Explain the difference between speed
and acceleration.
GETTING STARTED
Time 100 minutes
Setup and Materials
Materials for each group
yy Physics stand*
yy Gravity Drop catcher and dropper
yy CPO Timer with 2 photogates*
yy Plumb line
yy Steel marble
yy Metric ruler*
yy Calculator*
*provided by the teacher
O
nline Resources
Available at curiosityplace.com
yy Equipment Videos: Gravity Drop, CPO Timer
yy Skill and Practice Sheets
yy Whiteboard Resources
yy Animation: Acceleration Graph
yy Science Content Video: Speed vs. Time Graphs
yy Student Reading: Acceleration
1. Make copies of investigation sheets for students.
2.
W
atch the equipment video.
3. Review all safety procedures with students.
NGSS Connection This investigation builds conceptual understanding and skills for the following performance expectation.
HS-PS2-4. Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the
gravitational and electrostatic forces between objects.
Science and Engineering Practices
Using Mathematics and Computational Thinking
Disciplinary Core Ideas
PS2.B: Types of Interactions
Crosscutting Concepts
Patterns
Gravity Drop
29
Speed, Acceleration, and Free Fall
Vocabulary
acceleration – the change in speed over time
experiment – a procedure carried out under controlled
conditions to test a hypothesis
free fall – occurs when an object is accelerating due to
the force of gravity and no other forces are acting upon
that object
hypothesis– a possible explanation that can be tested by
comparison with scientific evidence
percent error – the difference between an approximate
or measured value and an exact or known value,
expressed as a percent of the known value
slope – the ratio of the vertical distance to the horizontal
distance that separates any two points on a line
speed – a measure of the distance traveled in a given
amount of time
trend line – a line that represents the general
relationship among data on a graph
BACKGROUND
Objects in free fall on Earth accelerate downward,
increasing their speed by 9.8 m/s2 every second.
The graph below shows data for the speed over time
of an object in free fall. We know that the object has a
constant acceleration because the shape of the graph
is a straight line. Constant acceleration means that an
object’s speed changes by the same amount over a given
time interval.
Free fall speed vs. time
50
Time (s)
Speed (m/s)
40
30
20
10
0
0
1
2
3
Time (s)
30 4
5
Speed (m/s)
0
0
1
9.8
2
19.6
3
29.4
4
39.2
5
49.0
In this investigation, students use the Gravity Drop to
investigate the speed of the marble at different points
along its downward path. The act of dropping the marble
past the photogates is a single event in time. Students
cannot measure every change in the marble’s motion
that occurs during this event. However, by repeating
similar events, such as dropping the marble from the
same height several times, students can gather data and
infer what happens to the marble’s motion each time
it falls.
These inferences are captured by creating a graph
that relates the observations of the marble’s speed at
photogate B to the time for which the marble has been
falling. In this way, the graph that students create is a
model of the change in speed, or the acceleration,
a marble will likely experience during its downward
travel. Looking at this model, students can verify their
hypothesis and make predictions about future drops
of the marble. The process of repeatedly dropping the
marble is an experiment designed to test student
hypotheses about the motion of a falling object.
Once students have measured the speed of the falling
marble at several points, they can plot their data and fit a
trend line to their graphs. From this trend line, students
can estimate the marble’s acceleration. Then, the
investigation asks students to use the algebraic equation:
y variable
slope
x variable
y = mx + b
y intercept
vB = at AB + v A
By substituting values for velocity, time, and slope into
the equation, students can calculate the speed of the
marble at different points. Finally, students can compare
their calculated values with experimentally-found values
and calculate percent error to check the accuracy of
their data.
B2
5E LESSON PLAN
Engage
Draw the following three graphs on the board:
Graph A
Graph B
Graph C
Speed
(cm/s)
Time (s)
Time (s)
Time (s)
Explain to students that these graphs show the motion of
an object over time. Ask students to describe the motion
of the object in each graph. Then ask students to suggest
different objects whose motion might be similar to these
graphs. Answers will likely vary. Accept all reasonable
answers. Students should be able to identify that speed
is increasing in graph A, staying constant in graph B,
and decreasing in graph C. This Engage activity can be
used as a formative assessment to determine student
readiness for the graphing activities in this investigation.
Science Content Video
Speed vs. Time Graphs
Animation
Acceleration Graph
Elaborate
Explore
In working with the gravity drop, students learn quickly
that they need to pay attention to their dropping
technique. More often than not, students will obtain
results that indicate some experimental error, which
can generally be attributed to a misalignment between
the diameter of the marble and the beams of the
photogates. The percent difference between your
acceleration value and 9.8 m/s2 indicates the percent
error in the experiment. This is explained in Part 7 of
the investigation.
Have students complete Investigation B2, Speed,
Acceleration, and Free Fall. Students apply their
knowledge to examine the speed of the marble at
several points along its path. With this information, they
determine how the speed of the falling marble changes
over time.
Identifying and controlling errors in measurement is an
important scientific practice. Consider using Part 7 to
conduct a class discussion about error and experimental
design. Alternatively, you may have students conduct
trials of this investigation with the specific goal of
examining error in their technique.
Explain
Evaluate
Revisit the Key Question to give students an opportunity
to reflect on their learning experience and verbalize
understandings about the science concepts explored in
the investigation. Curiosityplace.com resources, including
student readings, videos, animations, and whiteboard
resources, as well as readings from your current
science textbook, are other tools to facilitate student
communication about new ideas.
yy D
uring the investigation, use the checkpoint
questions as opportunities for ongoing assessment.
yy A
fter completing the investigation, have students
answer the assessment questions on the Evaluate
student sheet to check understanding of the
concepts presented.
Gravity Drop
31
Speed, Acceleration, and Free Fall
Explore
INVESTIGATION
B2
Name ____________________________________________ Date ________________________
B2 Speed, Acceleration, and Free Fall
Materials:
✔ Physics stand
✔ Gravity Drop catcher and
How does gravity affect the motion of a falling object?
dropper
Earth’s gravity pulls objects downward toward the center of Earth. In
Investigation B1, you learned how to measure the speed of a falling marble. ✔ CPO Timer and 2 photogates
In this investigation, you will apply your knowledge to examine the speed
✔ Plumb line
of the marble at several points along its path. With this information, you can
✔ Steel marble
determine how the speed of the marble changes as it falls.
✔ Metric ruler
✔ Calculator
Formulating a hypothesis

a. If you dropped a stone off a bridge into a river, how would you describe the motion of the falling stone?
Does the speed of the stone change during the fall?
Explore
INVESTIGATION
B2
Setting up the experiment

1. Attach the catcher at the first hole of the physics stand.
2. Attach the dropper at the nineteenth hole of the physics stand.
3. Attach photogate A at the seventeenth hole of the physics stand.
4. Attach photogate B so that it is 5 cm below photogate A. This will be
at the sixteenth hole of the physics stand.
5. Connect photogates A and B to the timer. Set the timer to interval
mode.
6. Use the plumb line to align the dropper and catcher. Adjust the
physics stand if necessary.
7. Use the steel marble to conduct a test drop and ensure that the
dropper and catcher are aligned. If necessary, repeat Steps 6 and
7 until you obtain a good drop. Check the display on the timer to
ensure that the photogates are recording time intervals, or “times,”
accurately.
Conducting the experiment

As the stone falls, its speed steadily increases until it hits the water.
b. What about a marble in free fall? An object is in free fall if it is accelerating due to the force of gravity
and no other forces are acting on it. In this investigation, you will measure the speed of a steel marble at
certain places along its path. Do you think the speed of the marble will change as it falls? If so, how will
the speed change? Be sure to include the term free fall in your answer.
Sample answer: The speed of a marble in free fall will steadily
increase until it lands in the catcher.
1. Begin Trial 1. Drop the steel marble until you get a good drop. In
Table 1, record the time registered by photogate A (tA ). Then record
the time registered by photogate B (tB ). Finally, record the time
registered when the marble passed from photogate A to photogate
B (tAB ).
2. For Trial 2, move photogate B so that it is 10 cm below photogate
A. Again, drop the steel marble until you get a good drop and
then record the times registered by the photogates.
3. Complete trials 3-15. Continue to drop the marble and record data
using the same process as in Step 2. Be sure to move photogate B
to the distances indicated in Table 1 for each trial.
Your answer to question b. is your hypothesis because you are making a prediction about the way the marble
will move before you measure its motion. A scientist uses a hypothesis to guide his or her investigation. A
hypothesis is tested with an experiment.
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B2 Speed, Acceleration, and Free Fall
Gravity Drop
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B2 Speed, Acceleration, and Free Fall
Gravity Drop
Guiding the INVESTIGATION
Guiding the INVESTIGATION
 Formulating a hypothesis
 Setting up the experiment
The investigation asks students to think about
changes in motion before introducing the term
acceleration. This is done for two reasons: First, to
ensure that when students learn the concept of
acceleration, their learning is firmly grounded in a
physical event. Second, the term acceleration has
connections to non-scientific uses in speech. For
instance, students may have heard of the accelerator
in a car. If students associate terms like accelerator with
speed, then this language association may strengthen
the misconception that acceleration is the same as
speed. Be alert as students develop their hypotheses.
If they already think acceleration is speed, it will likely
show up in the hypotheses they develop.
This investigation assumes that students learned to
align the dropper and catcher, and properly release
the marble from the dropper, during Investigation
B1. If students have not completed B1, or if time
has passed since that investigation, they may have
difficulty completing Part 2. If students exhibit
difficulty, consider having students review B1.
32 B2
Explore
INVESTIGATION
B2
Diameter
of marble
(cm)
1
5
1.90
2
10
1.90
3
15
1.90
4
20
1.90
5
25
1.90
6
30
1.90
7
35
1.90
8
40
1.90
9
45
1.90
10
50
1.90
11
55
1.90
12
60
1.90
13
65
1.90
14
70
1.90
15
75
1.90
.
Time A
tA
Speed at A
vA
Time B
Speed at B
(s)
(cm/s)
tB
vB
(s)
(cm/s)
0.0182
0.0183
0.0181
0.0183
0.0185
0.0185
0.0185
0.0183
0.0187
0.0188
0.0186
0.0185
0.0187
0.0186
0.0188
104.40
103.83
104.97
103.83
102.70
102.70
102.70
103.83
101.60
101.06
102.15
102.70
101.60
102.15
101.06
0.0129
0.0108
0.0090
0.0079
0.0075
0.0070
0.0066
0.0056
0.0060
0.0057
0.0052
0.0049
0.0051
0.0047
0.0046
147.29
175.93
211.11
240.51
253.33
271.43
287.88
339.29
316.67
333.33
365.39
387.76
372.55
404.26
413.04
Time from
A to B,
tAB
(s)
0.0422
0.0745
0.1049
0.1293
0.1523
0.1728
0.19
0.2075
0.2261
0.2407
0.2563
0.2713
0.2843
0.2986
0.3109
Calculating speed

The speed of the marble at either photogate is calculated by dividing the marble’s diameter by the time the light
beam was broken as the marble dropped through the photogate. The diameter of the marble is 1.90 centimeters.
Using the speed equations below, calculate the speed of the marble at photogates A and at B. Record your
results in Table 1.
1.9 cm
1.9 cm
Speed at A, v A =
Speed at B, v B =
Time at A, t A
Time at B, t B
Speed values are recorded in Table 1.
Graphing the data

Create a graph of the data. A graph gives you a “picture” of the motion of the marble as it falls.
Speed vs. time for a falling marble
Using your data, answer the following:
a. What happens to the time it takes for the marble to fall through photogate B as the photogate is moved
closer and closer to the catcher?
As photogate B moves closer and closer to the catcher, it is moving
farther and farther away from the starting point of the dropped
marble. The time gets shorter and shorter because it takes less time
for the marble to pass through the photogate as the marble travels
downward.
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B2
The times at A are all nearly the same. This makes sense, because
photogate A was in the same place for all drops. The times at B get
shorter and shorter as photogate B moves farther and farther away
from the dropper.
Speed of the marble at B (cm/s)
Distance
between
photogates
(cm)
INVESTIGATION
b. Compare the times registered at photogate A and the times registered at photogate B. Are they the same
or different? Do you see a pattern? If so, what is it?
Sample data:
Table 1: Falling marble data
Trial
Explore
B2 Speed, Acceleration, and Free Fall
Gravity Drop
What does a graph
of the motion of
a falling marble
look like?
Falling time A to B (s)
1. Make a graph with speed of the marble at B on the y-axis and the time from A to B on the x-axis.
2. When you finish plotting the data, draw a trend line. A trend line is a line that represents the general
relationship between data points on a graph. Begin the trend line at the same x-coordinate as the first data
point in the graph. End the line at the last x-coordinate in the graph. Position and angle your trend line so
that it passes through or between as many of the data points as possible.
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B2 Speed, Acceleration, and Free Fall
Gravity Drop
TEACHING TIP
Speed and velocity In this investigation, units
of speed, or velocity, are given in centimeters per
second (cm/s). Physics often draws a distinction
between speed and velocity where speed is
considered a scalar, or rate, while velocity is
considered a vector. A vector is a measurement
that implies both a rate and an orientation or
direction. For this investigation, this distinction isn’t
necessary because the Gravity Drop doesn’t change
the direction, or orientation, of the marble’s travel.
Both values are generally represented with the
symbol v in calculations, and that is the convention
used here.
Gravity Drop
33
Speed, Acceleration, and Free Fall
Explore
INVESTIGATION
B2
Explore
INVESTIGATION
B2
Drawing conclusions

a. Was the hypothesis you formulated in Part 1 correct? Explain.
Sample answer: The speed-versus-time graph shows that my
hypothesis was correct. As the time from A to B increases (as
photogate B is moved down the pole), the speed at B increases.
b. The terms speed and acceleration are often used to describe motion. The term acceleration means a change
in speed over time. Based on this definition, was the marble accelerating as it fell? Explain your answer.
Yes, the marble was accelerating as it was falling because the speed
of the marble was changing.
y-label:
c. What did you notice about the speeds at A?
The speed at A stayed almost the same for each trial.
d. If there were changes in the speeds found at photogate A, what might this tell you?
x-label:
Answers may vary. Variation in the speeds found at A would indicate
that students used an inconsistent dropping technique.
See Part 5 sample graph.
a. What is the general shape of the data in the graph? What does the graph show you about the motion of
the falling marble?
Looking from left to right, in general, the data falls along a linear
path. The data shows that the speed of the marble increases at a
steady rate over time.
b. Looking at the graph, what is happening to the motion of the marble in free fall?
The graph shows that as the time increases from A to B, the speed
of the marble increases at photogate B. This means that the marble
is speeding up over time.
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Can be duplicated for classroom use
B2 Speed, Acceleration, and Free Fall
Gravity Drop
5 of 10
Developing a model

In science, graphs and equations can be used to develop a model of the forces acting on an object like the
marble in the Gravity Drop. One advantage of having these models is that they can be used to predict future
events. For instance, imagine if you wanted to know what the speed of the marble might be if it fell farther
than the total height of the physics stand. With a model that accurately simulated the Gravity Drop, you could
predict that speed. Another advantage of a model is that it can confirm an outcome for a set of conditions that
you have actually measured. For instance, you could use a model of the Gravity Drop to predict the speed
of the marble under the same conditions as one of the trials you conducted earlier. Then it would be possible
to compare the measured values to the modeled values of speed, and this comparison may help to identify
measurement errors. The values predicted by a model should generally match those measured in an experiment,
but if one or more measurements varies significantly from the model, and that model has a good fit with the
other data, then it is likely some sort of measurement error has occurred. Based on this, you might change your
procedure to avoid that type of error.
Developing a model of the Gravity Drop begins with the trend line. The trend line gives you a way to estimate
the marble’s acceleration using the concept of slope. Slope is the ratio of the vertical distance to the horizontal
distance that separates any two points on a line. Sometimes slope is called “rise over run” because when it is
shown as a fraction, the vertical displacement between the two points, or “rise,” appears as the numerator and
the horizontal displacement, or “run,” is the denominator. In the trend line you made on your speed vs. time
graph, slope is the marble’s acceleration. Before you estimate the slope of your trend line, let’s look at a sample
graph. The graph below is made from four points of data.
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B2 Speed, Acceleration, and Free Fall
Gravity Drop
Part 5 sample graph
Speed of the Marble at B (cm/s)
Speed of marble at B vs. time from A to B
500
450
400
350
300
250
200
150
100
50
0
0.00
0.05
0.10
0.15
0.20
Falling Time A to B (s)
34 0.25
0.30
0.35
B2
Explore
INVESTIGATION
B2
200
100 cm/s
= 1052.6 cm/s 2
0.095 s
150
100
a. What is the value for the slope of the line on your speed vs. time graph? Show your work on your own
graph.
50
0
0
0.05
0.10
0.15
See 7a sample graph.
0.20
Time (s)
Distance between
photogates
(cm)
acceleration
b. The slope of the line on any speed vs. time graph is equal to the object’s _____________________.
Time from
A to B
(s)
Speed at B
(cm/s)
1
5
0.0422
147.286822
2
10
0.0745
175.925926
3
15
0.1
172.727273
4
20
0.13564
240.536777
To estimate the slope of the trend line, compare the positions of any two points along the line. Often, choosing
the points where the trend line intersects grid lines from the vertical and horizontal axes of the line is the
simplest way to accomplish this.
Part 7 sample graph
250
200
Using the graph to check measured values

As mentioned in Part 7, a graph can be used to check the measurement accuracy for a system like the Gravity Drop.
The equation for a line on a graph is:
y variable
slope
x variable
y = mx + b
y intercept
If you substitute the specific variables from your speed vs. time graph into the linear equation, the equation will
appear like this:
vB = at AB + v A
This equation uses slightly different symbols than are found in the linear equation above. In science, speed and
velocity are often shown with the symbol v. Meanwhile, acceleration is shown with the letter a. This equation
can be used to predict the speed of the marble as time passes.
Using your values for the y-intercept ( vA ), slope (a), and time ( tAB ), calculate the speeds of the marble at B
(vB ). For each trial, or row, of Table 1, you can use the values of speed at A, slope, and time from A to B to
calculate the speed at B. Record your calculated speeds in Table 2.
300
Speed (cm/s)
B2
The next value to be found is the vertical distance, or “rise.” The lowest point of the trend line is found around
140 and the highest is found at about 240, giving us a rise of 100. Here is our resulting slope:
250
Speed (cm/s)
INVESTIGATION
Starting with the horizontal dimension of the trend line, we find that the line extends from roughly 0.040 to
0.135. On the graph, these coordinates are rearranged so that the resulting difference is a positive number, and
the result is 0.095. This is the horizontal distance, or “run,” value in the slope.
Part 7 sample graph
300
Trial
Explore
See Part 8, Trial 1 sample answer.
240 – 140 = 100
150
0.135 – 0.040 = 0.095
100
50
0
0
0.05
0.10
0.15
0.20
Time (s)
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B2 Speed, Acceleration, and Free Fall
Gravity Drop
7 of 10
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7a sample graph
Speed of the marble at B (cm/s)
450
slope =
400
265.8733 cm/s
= 989.48 cm/s 2
0.2687 s
(0.3109, 413.5793)
According to Table 1,
v A = 104.40 cm/s
t AB = 0.0422 s
According to Part 7,
350
300
(413.5793 – 147.7061 = 265.8733)
250
a = 989.40 cm/s 2
Solving for v B using the values above,
v B = at AB + v A
200
v B = (989.40 cm/s 2 )(0.0422 s) + 104.40 cm/s
(0.3109 – 0.0422 = 0.2687)
150
100
v B = 146.133 cm/s
(0.0422,147.7061)
50
0
B2 Speed, Acceleration, and Free Fall
Gravity Drop
Part 8, Trial 1 sample answer
Speed vs. time
500
8 of 10
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Falling time A to B (s)
Gravity Drop
35
Speed, Acceleration, and Free Fall
Explore
INVESTIGATION
Explore
B2
Acceleration
(cm/s2)
Time from
A to B
(s)
Speed at A
(cm/s)
1
989.046
0.0422
2
989.046
3
B2
a. How do your calculated values compare with the line that represents the measured values?
Table 2: Calculating speed
Trial
INVESTIGATION
Answers will vary. Sample answer: The calculated values fall on the
line that was drawn through the experimental values.
Calculated speed at B
(cm/s)
Measured speed
at B
104.3956
146.133345
147.2868
0.0745
103.8251
177.5090626
175.9259
989.046
0.1049
104.9724
208.7232997
211.1111
4
989.046
0.1293
103.8251
231.7087827
240.5063
5
989.046
0.1523
102.7027
253.3344064
253.3333
6
989.046
0.1728
102.7027
273.6098492
271.4286
Percent error

7
989.046
0.19
102.7027
290.6214401
287.8788
8
989.046
0.2075
103.8251
309.0521788
339.2857
We said above that gravity on Earth causes objects to accelerate at about 9.8 m/s2. How much error was there
between your measurements of gravity using the Gravity Drop and this figure? To answer this question, you
can calculate percent error. Percent error is often used in science to determine the accuracy of a test.
9
989.046
0.2261
101.6043
325.2275756
316.6667
10
989.046
0.2407
101.0638
339.1271987
333.3333
11
989.046
0.2563
102.1505
355.643024
365.3846
12
989.046
0.2713
102.7027
371.0308788
387.7551
13
989.046
0.2843
101.6043
382.790052
372.549
14
989.046
0.2986
102.1505
397.4796692
404.2553
15
989.046
0.3109
101.0638
408.558227
413.0435
b. What are some possible explanations for any differences between the measured and the calculated values
of velocity?
Answers will vary. Sample answer: The calculated and the accepted
value are very close. The acceleration value I calculated is
989.046 cm/s2. This value is higher than the accepted value for the
acceleration of gravity, 980.0 cm/s2. There is about a 1% difference
between these two values.
Percent error can be found using this equation:
Exact value - found value
× 100 = % error
Exact value
a. In this case, the acceleration of gravity, 9.8 m/s2 is the exact value because it has been found through
many independent experiments. Meanwhile, the value of slope you found experimentally is the “found
value.” Calculate the percent error of your findings.
trend line slope = 989.48 cm/s 2
Converting cm/s 2 to m/s 2 :
1m/s 2
= 9.8948 m/s 2
100 cm/s 2
Expressing slope as a percentage of gravity (9.8 m/s 2 ) :
989.48 cm/s 2 ×
1. Plot the times and calculated speeds on your speed vs. time graph. Use a different color to distinguish the
calculated speeds from the measured speeds.
See Part 8 sample graph.
9.8 m/s 2 − 9.8948 m/s 2
9.8 m/s 2
Copyright © CPO Science
Can be duplicated for classroom use
9 of 10
B2 Speed, Acceleration, and Free Fall
Gravity Drop
Copyright © CPO Science
Can be duplicated for classroom use
× 100 = 0.967347%, about 1%
10 of 10
B2 Speed, Acceleration, and Free Fall
Gravity Drop
Part 8 sample graph
Speed vs. time with calculated speed at B and measured speed at B
Speed of the Marble at B (cm/s)
450
400
350
300
250
Speed of marble at B
vs. time from A to B
200
Calculated speed at B
150
100
50
0
36 0.05
0.10
0.15
Time A to B (s)
0.20
0.25
0.30
0.35
Evaluate
B2
INVESTIGATION
B2
Notes and Reflections
Name ____________________________________________ Date ________________________
1. In your own words, explain the difference between speed and acceleration.
Answers may vary. Students should understand that speed is the
rate of change of position for an object. Acceleration is the rate of
change of speed for an object.
2. Four photogates are attached to four timers that each measure the time
for the marble to fall through the light beam (shown at right). Which
photogate goes with which timer?
1: D
2: B
3: C
4: A
3. The data table below shows results from a typical Gravity Drop
experiment. Which trend line in the graph indicates the speed versus
time relationship indicated in the table below? Choose A, B, C, or D.
Note: speeds are in m/s.
Distance A to B
(m)
Speed at A
(m/s)
Speed at B
(m/s)
Time A to B
(s)
4.50
4.00
1.005
1.769
0.0783
1.000
2.247
0.1305
0.30
1.000
2.653
0.1724
0.40
1.005
3.081
0.2086
0.50
1.000
3.351
0.2409
1.50
0.60
1.000
3.604
0.2703
1.00
0.00
0.70
1.000
3.898
0.2977
Speed at B (m/s)
0.10
0.20
3.50
Speed vs. time
B
A
C
3.00
2.50
D
2.00
0.10
0.20
0.30
Time from A to B (s)
Line B represents the correct relationship.
4. A student completes a single trial using the Gravity Drop and two photogates. The student obtains the
following data:
Trial
1
Distance between
photogates (cm) Acceleration (cm/s2) Time from A to B (s)
5
989.046
0.5
Speed at A (cm/s)
Predicted Speed at B (cm/s)
104.3956
598.9185976
Use the information in the table to predict the speed of the marble at B. Be sure to show your work on the
reverse side of this sheet.
See Question 4 sample answer.
B2 Speed, Acceleration, and Free Fall
Gravity Drop
Copyright © CPO Science
Can be duplicated for classroom use
Question 4 sample answer
According to Table 1,
v A = 104.40 cm/s
t AB = 0.0422 s
According to Part 7,
2
a = 989.40 cm/s
Solving for v B using the values above,
v B = at AB + v A
v B = (989.40 cm/s 2 )(0.0422 s) + 104.40 cm/s
WRAPPING UP
Have your students reflect on what they
learned from the investigation by answering the
following questions:
1. What is the difference between an object’s
acceleration and an object’s speed?
2. What is the shape of a graph that describes the
motion of a falling marble?
3. How can a graph be used to predict the speed of
an object in free fall?
v B = 146.133 cm/s
Gravity Drop
37
Speed, Acceleration, and Free Fall
Notes and Reflections
38