Name: ______________________________ Date: _____________ Period: __________ ID: _________
General Physics
Unit 2 – Speed and Graphing
Vocabulary
Term
Distance
Displacement
Position
Average Speed
Average Velocity
Instantaneous Speed
Acceleration
Definition
Section 1.3 Speed (pages 17-21)
Speed
What is it?
(definition)
Measurement
Speed
Distance
time
Symbol
s
d
t
Units
Meters/second
Meters
seconds
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Velocity
What is it?
(definition)
Measurement
velocity
displacement
time
Symbol
v
d
t
Units
Meters/second
Meters
seconds
Equation
v = d/t
d=vxt
t = d/v
Gives you . . .
Speed
Distance
Time
If you know . . .
Distance and time
Speed and time
Distance and speed
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Acceleration
What is it?
(definition)
∆v = vf - vi
If an object is
accelerating then it
is either
Measurement
acceleration
Change in velocity
time
Symbol
a
∆v
t
Units
meters/second2
meters/second
seconds
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Speed & Velocity Examples
1.
If you start from the Art Gallery and travel to the Cafe and back to the Art Gallery in 7200 seconds:
a. What is the distance you travel?
b.
What is your displacement?
c.
What is your average speed?
Looking For
Given
Average Speed
Distance traveled =
Relationship
Solution
Relationship
Solution
time =
d. What is your average velocity?
Looking For
Given
Average Speed
Distance traveled =
time =
2.
If you start from the Art Gallery and travel to the Cafe in 3600 seconds:
a. What is the distance you travel?
b.
What is your displacement?
c.
What is your average speed?
Looking For
Given
Average Speed
Distance traveled =
Relationship
Solution
Relationship
Solution
time =
d. What is your average velocity?
Looking For
Given
Average Speed
Distance traveled =
time =
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3.
If you start from the Bakery, travel to the Cafe, and then to the Art Gallery in 120 seconds,
a. What is the magnitude of your displacement?
b.
What distance did you travel?
c.
What is your average speed?
Looking For
Given
Average Speed
Distance traveled =
Relationship
Solution
Relationship
Solution
time =
d. What is your average velocity?
Looking For
Given
Average Velocity
displacement =
time =
4.
Sketch your own example of a situation where a person/object travels with the same average speed and
average velocity.
5.
Sketch your own example of a situation where a person/object travels in two different directions and has
a different displacement and distance.
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Acceleration Examples
1. A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s
acceleration?
Looking For
Acceleration of
the skater
Given
Relationship
Solution
Beginning speed = 2.0 m/s
Final speed = 10.0 m/s
Change in time = 3 seconds
The acceleration of the skater is 2.7 meters per
second per second.
2. A car accelerates at a rate of 3.0 m/s2. If its original speed is 8.0 m/s, how many seconds will it
take the car to reach a final speed of 25.0 m/s?
Looking For
The time to reach
the final speed.
Given
Relationship
Solution
Beginning speed = 8.0 m/s; Final
speed = 25.0 m/s
Acceleration = 3.0 m/s2
`
The time for the car to reach its final speed is 5.7
seconds.
1.
While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the
automobile’s acceleration? (Remember that a negative value indicates a slowing down or deceleration.)
Looking For
2.
Relationship
Solution
A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45 m/s in a
period of 4.5 seconds. What is the acceleration of the dragster?
Looking For
3.
Given
Given
Relationship
Solution
A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop. How much
time will it take for the car to stop if it decelerates at -4.0 m/s2?
Looking For
Given
Relationship
Solution
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4.
A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of this
helicopter?
Looking For
Given
Solution
d
d
s
Relationship
t
v
∆v
t
a
t
Class Work
5.
6.
What is the average speed of a cheetah that sprints 100 m East in 4 s?
Looking For
Given
Relationship
Solution
What is the cheetah’s average velocity?
Looking For
Solution
Relationship
A runner makes one lap around a 400 m track in a time of 25.0 s. What was the runner's average speed?
Looking For
Given
Relationship
Solution
What is the runner’s average velocity?
Looking For
7.
Given
Given
Relationship
Solution
A soccer field is about 120 m long. If it takes Alex 10 seconds to run its length, what is his average speed?
Looking For
Given
Relationship
Solution
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8.
Calculate the average velocity of a car that drives 50 meters North East in 25 seconds.
Looking For
Given
Relationship
Solution
9.
How long would it take you to run across the high school parking lot if the lot is 50 meters long and you run with an
average speed of 5 m/sec?
Looking For
Given
Relationship
Solution
10.
Bart ran 5000 meters from the cops and an average velocity of 6 meters/second West before he got caught. How long
did he run?
Looking For
Given
Relationship
Solution
d
d
s
t
v
∆v
t
a
t
Group Work
11. What is the average speed of a cheetah that travels 112.0 meters South in 4.0 seconds? What is the cheetah’s average
velocity?
Looking For
Given
Relationship
Solution
12. Samantha runs a 400 m lap in 53.5 s. What is her average speed? What is her average velocity?
Looking For
Given
Relationship
Solution
13. What is the average speed of a car that traveled 300.0 meters North West in 3600 seconds? What is the cars average
velocity?
Looking For
Given
Relationship
Solution
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14. Elmer Fudd shoots a bullet from his rifle with an average speed of 720.0 m/s. What time is required to strike a target
324.0 m away?
Looking For
Given
Relationship
Solution
d
d
s
t
v
∆v
t
a
t
Homework
1.
On a baseball diamond, the distance from home plate to the pitcher’s mound is 18.5 m. If a pitcher is capable of
throwing a ball with an average speed of 38.5 m/s, how much time does it take a thrown ball to reach home plate?
Looking For
Given
Relationship
Solution
2.
A bullet travels with an average velocity of 850 m/s. How long will it take a bullet to go 1000 m?
Looking For
Given
Relationship
Solution
3.
Every summer Mr. Magoo drives to Michigan. It is 3900 m to get there. If he drives with an average speed 100 m/s,
how much time will he spend driving?
Looking For
Given
Relationship
Solution
4.
What is the average speed of a cheetah that travels 112.0 meters South in 4.0 seconds? What is the cheetah’s average
velocity?
Looking For
Given
Relationship
Solution
5.
After traveling for 6.0 seconds, a runner reaches a speed of 10 m/s. What is the runner’s
acceleration?
Looking For
Given
Relationship
Solution
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Challenge Problems
1.
It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French class for the third time this
week. She must get from one side of the school to the other by hurrying down three different hallways. She runs
down the first hallway, a distance of 35.0 m, at a speed of 3.50 m/s. The second hallway is filled with students, and
she covers its 48.0 m length at an average speed of 1.20 m/s. The final hallway is empty, and Suzette sprints its 60.0 m
length at a speed of 5.00 m/s. Does Suzette make it to class on time or does she get detention for being late again?
Show all of your work.
Given
Formula
Set-up
Solution
2.
During an Apollo moon landing, reflecting panels were placed on the moon. This allowed earth-based astronomers
to shoot laser beams at the moon's surface to determine its distance. The reflected laser beam was observed 2.52 s
after the laser pulse was sent. The speed of light is 3.0  108 m/s. What was the distance between the astronomers and
the moon?
Given
Formula
Set-up
Solution
3.
For many years, the posted highway speed limit was 88.5 km/hr (55 mi/hr) but in recent years some rural stretches of
highway have increased their speed limit to 104.6 km/hr (65 mi/hr). In Maine, the distance from Portland to Bangor
is 215 km. How much time can be saved in making this trip at the new speed limit?
Given
Formula
Set-up
Solution
4.
The tortoise and the hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000. m
distance at a speed of 0.2000 m/s while the rabbit runs the first 200.0 m at 2.000 m/s The rabbit then stops to take a
nap for 1.300 hr and awakens to finish the last 800.0 m with an average speed of 3.000 m/s. Who wins the race and by
how much time?
Given
Formula
Set-up
Solution
5.
Two physics professors challenge each other to a 100. m race across the football field. The loser will grade the
winner's physics labs for one month. Dr. Rice runs the race in 10.40 s. Dr. De La Paz runs the first 25.0 m with an
average speed of 10.0 m/s, the next 50.0 m with an average speed of 9.50 m/s, and the last 25.0 m with an average
speed of 11.1 m/s. Who gets stuck grading physics labs for the next month?
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Activity – Toy Car
General Physics
Research Question
 What is the relationship between position and time for a moving object?
 What does the slope of a position vs. time graph represent?
 How can we determine if an object moves with constant speed?
Constant speed: The same amount of distance is covered each second.
Hypothesis
As time increases the distance a toy car travels will (increase, decrease, remain the same).
Procedure
1. Choose a starting point for your car. Mark this point with masking tape, and label it “starting
point.”
2. Start the car, and place it on the starting point. Release the car (your lab partner should start the
stopwatch at the same time). Let the car move in a straight line for 2.0 s. Repeat for several
trials, until you find the point that the car consistently crosses after 2.0 s. Mark this point with
masking tape, and label it “0.00 m.” Throughout this experiment, you will start the car at the
original starting point, but you will begin to measure the distance and time of the car’s motion
when the car crosses the 0.00 m mark.
3. Start the car, and place it on the floor at the starting point. Observe the car as it moves. Be sure
to start the stopwatch as the car crosses the 0.00 m mark.
4. After 10.0 s, mark the position of the car with the masking tape. Label this mark “10.0 s.”
5. Repeat steps 3 and 4 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. Be sure to label
each point according to how much time it took for the car to get to that point from the 0.00 m
mark.
6. Use the meter stick to measure the exact position from the 0.00 m mark to each time position
mark. (Do not measure the distance from the starting point.)
7. For each position marked with tape record in Table 1 on the next page
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Research Question
The research questions of this activity was to
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
Hypothesis
I predicted as time increases the distance a toy car travels will (increase, decrease, remain the same) because
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
Data
Table 1: Position vs. Time
Time (sec)
Position (m)
0
1
2
3
4
5
6
7
8
9
10
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Position vs. time
Position
(meters)
Average time (seconds)
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Conclusion
Directions: Answer the following questions in complete sentences.
1) What was the shape of the line on your graph, curved or straight?
______________________________________________________________________________
______________________________________________________________________________
2) Does the shape of your line agree with your hypothesis?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3) Did your vehicle move at a constant speed? How do you know?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4) What variable did you plot on the y-axis on your graph?
5) What variable did you plot on the x-axis on your graph?
6) Slope refers to the steepness of a line or surface and is found by dividing the change in your
vertical axis (rise) over the change in your horizontal axis (run).
The slope of your graph is equal to: answer to #4/answer to #5
Answer to #4 
Answer to #5 
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Graphing Little Dudes
General Physics
Suppose something is moving. If you collect corresponding clock reading and position measurements, these numbers
form ordered pairs that can easily be graphed. Consider the various little dudes shown below. They exist and move
along a sidewalk marked in 1 meter increments. We are given snapshots 2-second time intervals.
2
4
6
8
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Analysis
1. Draw the line of the graph and label the line, “Walking Dude.”
2. What is the independent variable on the graph?
3. What is the dependent variable on the graph?
4. What does the notation Δ t mean and what is Δ t between 4s and 6s?
5. What does the notation Δ x mean and what is Δ x on the graph between 4s and 6s?
6. What relation can you use to find the slope of the graph, in terms of rise and run?
7. What quantity represents rise on our graph? What represents run?
8. What equation would you use to determine the slope of a position vs. clock reading graph? (Do not use
any numbers yet, simply state the equation.) Does this equation look familiar? If not, it is wrong; if so,
where have you seen it before?
9. Apply the equation and determine the slope of Walking Dude’s position vs. clock reading graph.
10. On the axes on the front, plot position vs. clock reading for the two other little dudes shown below.
Running Dudette starts at 0m and 0s. Reading Dude starts at 8m and 0s. Don’t forget to label.
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Running Dudette
time
(seconds)
Position
(meters)
Speed
(m/s)
Position
(meters)
Speed
(m/s)
0
2
4
6
8
Reading Dude
time
(seconds)
0
2
4
6
8
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Qualitative graphs
x
(m)
(m/s)
t (s)
x
(m)
t (s)
(m/s)
t (s)
x
(m)
t (s)
(m/s)
t (s)
t (s)
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Walk This Way
Purpose
To develop an understanding of motion graphs by analyzing graphs made by walking in front of a motion
probe. You will use a motion probe to see what the graph of your motion looks like when you move with
increasing, decreasing and constant speed. To collect motion data using an ultrasonic motion detector and
analyze plots for evidence that verifies the rules of kinematics.
Research Question
__________________________________________________________________________________________
Hypothesis
Describe how you would walk to produce a graph of constant speed.
__________________________________________________________________________________________
__________________________________________________________________________________________
Describe how you would walk to produce a graph of increasing speed.
__________________________________________________________________________________________
__________________________________________________________________________________________
Describe how you would walk to produce a graph of decreasing speed.
__________________________________________________________________________________________
__________________________________________________________________________________________
Introduction
A motion probe sends out pulses of ultrasound and receives the echoes from objects in front of it. The motion
probe can be connected to a CBL and graphing calculator or to a computer with an interface (some motion
probes connect directly to a graphing calculator and need no CBL). When the object in front of the motion
probe moves, a graph of the motion of the object is displayed on the screen of the calculator. There are several
things you should keep in mind as you carry out this investigation:
1. The motion probe (or wall) is the origin or reference point from which distances are measured.
2. The motion probe detects the closest object directly in front of it (including your arms if you swing them
as you walk or anything close to your path).
3. The motion probe will not correctly measure anything closer than .5 m. When making your graphs don’t
go closer than .5 m from the motion probe.
4. A good way to make the motion graph is to hold the calculator, interface, and motion probe and point
the motion probe toward a wall. This will allow you to see the graph on the calculator screen as you
walk.
A plot of velocity versus time gives certain information about an object’s motion including how fast and in what
direction an object is moving and whether the object is speeding up or slowing down. It is also possible to
determine an object’s displacement using a velocity vs. time plot by computing the area underneath the graph
during a given interval of time. This property is true for a velocity vs time curve, regardless of its shape.
You will present your findings to the class.
Materials:
Computer interface and software, printer, masking tape, meter stick
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Procedure:
Part I: Graphing Position vs. Time
1. Start collecting data. At this point, the motion probe should start ticking and a graph should be drawn on
the computer. Try moving back and forth to see what effect this has on the graph.
2. Your group will be assigned one of the qualitative challenges below.
3. Have each group member try the challenge. After several trials show Mr. Beatty. Once he approves
your graph you can copy it on the next page.
4. You will then collaborate with a member from each group to get their qualitative graph. You each must
explain what you did to produce your graph.
Group
Qualitative Graph
Motion: You remain at rest (motionless) at the 2 meter mark from the detector.
A
B
Motion: You walk slowly from the 1 meter mark to the 3 meter mark.
C
Motion: You walk slowly from the 3 meter mark to the 1 meter mark.
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D
Motion: Starting at the 1 meter mark, you walk slowly to the 3 meter mark, then quickly back to the 1 meter
mark.
E
Motion: Starting at the 3 meter mark, walk quickly to the 2 meter mark. Wait there for 2-3 seconds, then walk
very slowly to the 0.5 meter mark.
Analysis:
1. Explain the significance of the slope of a distance vs. time graph. Include a discussion of positive and negative
slope.
2. What type of motion is occurring when the slope of a distance vs. time graph is zero?
3. What type of motion is occurring when the slope of a distance vs. time graph is constant?
4. What type of motion is occurring when the slope of a distance vs. time graph is changing?
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5. Acceleration is the rate of change of speed. When speed is constant acceleration is zero (no change means the rate
of change is zero). How does the slope of a distance vs. time graph change when there is acceleration?
6. Describe how a person would have to move to create a distance vs. time graph as pictured.
Part II: The Matching Challenge
1. Open the file “Position vs. Time”. Study it to determine the following:
a. How close should you be to the motion Sensor at the beginning?
b. How far away should you move?
c. How long should your motion last?
2. Walk the graph trying to duplicate the lines as precisely as possible.
3. Over the course of the next week you will be quizzed on your ability to produce the motions we have
discussed in this activity. You will be challenged with a graph similar to the matching challenge.
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Part II: For each graph have a group member walk matching each graph then describe their motion next to the
picture of the graph. Use word like faster, slower, going toward, going away, increasing speed, decreasing
speed, steeper, less steep.
Graph 1
4
3
Score:
2
1
0
0
5
10
15
20
Graph 2
4
3
Score:
2
1
0
0
5
10
15
20
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HOMEWORK FOR LAB 1:
INTRODUCTION TO MOTION
POSITION—TIME GRAPHS
Answer the following questions in the spaces provided.
1. What do you do to create a horizontal line on a
position—time graph?
2. How do you walk to create a straight line that
slopes up?
3. How do you walk to create a straight line that
slopes down?
4. How do you move so the graph goes up steeply at
first, and then continues up less steeply?
5. How do you walk to create a U-shaped graph?
Answer the following about two objects, A and B, whose motion produced the following
position—time graphs.
6.
a. Which object is
moving faster
A or B?
b. Which starts ahead?
Define what you
mean by “ahead.”
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c. What does the intersection mean?
7.
a. Which object is
moving faster?
b.
8.
Which object has a
negative velocity
according to the
convention we have established?
a. Which object is
moving faster?
b. Which starts ahead?
Explain what you
mean by “ahead.”
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Project - The Ford Challenge
General Physics
The Challenge
Design a car that is fast and safe. Your design modifications are limited to 5 sheets of paper, glue, axles, and
wheels.
Research Question
How can you calculate the speed of your car to determine if it is the fastest in the class? How can you
determine if your car accelerates the fastest?
Design Criteria
1. Your car can be made of only the following materials – 5 sheets of paper, 4 wheels, cut drinking straws
for the axle housings, and glue.
2. The drinking straw may only be used as axle housing. It cannot be used for any other structural element
of the car.
3. The car’s width must be less than 6.5 cm.
4. The car’s mass must be less than 30 grams.
5. There can be no physical contact between the device and the designer once the vehicle has been released
on the track.
6. The design must allow for easy removal and inspection of the egg. The egg will be provided by your
teacher, and will be put into the car when time has elapsed.
7. Repairs requiring additional materials will not be allowed once the competition has begun.
8. All vehicles must display the following: vehicle’s name, builder’s name, vehicle’s width in cm, and
vehicle’s mass in grams (without egg).
9. All vehicles must be decorated.
10. All vehicles must have a theme that is consistent with the way it is decorated.
11. Refer to the grading sheet. Ask your teacher for a copy. You will receive points for a unique design,
quality of construction, vehicle performance, accuracy of measurements, and completion of the lab
report.
The Race Part I
1. Time how long it takes the car to travel from the top to the bottom of the race track. Record the time (t)
for this trial (#1) in Data Table 1.
2. Conduct two more trials. Record your time (t) for each trial in Data Table 1.
3. Calculate the average time from start to finish. Record the average time of the run (t) in Data Table 2.
4. Compute the average speed (v) of your car by dividing the distance traveled by the race time
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Data Table 1
Trial #
1
Time to Travel Down Race Track (seconds)
2
3
Average
Given
Formula
Set Up (with units)
Solution (with
units)
Grading Criteria
50 points
Grading Categories
Points Earned
Design Plan (15 pts.): Is the design unique and
creative? Does the design resemble another student’s
in class?
Quality of construction (20 pts.): Does construction
show evidence of quality time and effort or of a last
minute rush job? Is the car decorated? Does the
vehicle have a theme? Do the decorations match them
theme of the car? Does the student use color to add to
the vehicle’s appearance? Does the student use more
than just colored pencils, crayons and markers to
decorate their car?
Car holds the egg and rolls entire track length (10 pts.)
Mass under 30 grams
(1 pt.)
Width under 6.5 cm
(1 pt.)
Data written on car
(1 pt.)
Sample Calculation Provided
(2 pts.)
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