Vocabulary
Term
Distance
Definition
A scalar quantity that refers to "how much ground an
object has covered" during its motion.
Displacement
A vector quantity that refers to "how far out of place an
object is"; it is the object's overall change in position.
Position
Where an object is located relative to a certain reference
point (usually in a coordinate system).
Average Speed
The rate at which position changes; the distance traveled
divided by the time taken. Refers to how fast an object
is moving and is always measured in a unit of distance
over a unit of time.
Average Velocity
The vector form of speed; a quantity that specifies both
speed and direction. The rate at which an object
changes its displacement/position and includes direction.
Instantaneous Speed
The speed of an object at any given instant.
Acceleration
The change of speed over time.
Page | 1
Homer walked as follows:
Starting at the 0,0 coordinate, he walked 12 meters east, 8 meters west, 10 meters
east.
West
-18 -16 -14 -12
•
•
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
16
His displacement was 14 meters east.
His distance traveled was 30 meters.
• His final position was +14 meters.
Using this information, define the following:
Displacement - A vector quantity that refers to "how far out of place an object
is"; it is the object's overall change in position.
Distance - A scalar quantity that refers to "how much ground an object has
covered" during its motion.
Position - Where an object is located relative to a certain reference point
(usually in a coordinate system).
Check Questions
What is the displacement of the cross-country team if they begin at the school, run
10 miles and finish back at the school? 0 miles
What distance did the cross-country team run? 20 miles
Sketch your own example of a situation where a person/object walks in three
different directions and has a different displacement, distance, and position
Page | 2
18 East
Peter Griffin needs to purchase a new tv. He resets his odometer when he
leaves his house heading South. When he arrives at Best Buy, the
odometer reads 30 miles. It took him exactly one hour to get there.
His average speed was 30 miles/hour. His average velocity was 30
miles/hour SOUTH. Using this information, define the following:
Average speed - Refers to how fast an object is moving and is always
measured in a unit of distance over a unit of time.
Average velocity - The rate at which an object changes its
displacement/position and includes direction.
Peter reset his odometer to come home. Again it was exactly 30 miles
and it took him 1 hour.
His average speed for the entire trip was 30 miles/hour. His average velocity was 0 miles/hour.
Using this information, revise the above definitions:
Average speed - The rate at which position changes; the distance traveled divided by the time
taken. Refers to how fast an object is moving and is always measured in a unit of distance over a
unit of time.
Average velocity - The vector form of speed; a quantity that specifies both speed and direction.
The rate at which an object changes its displacement/position and includes direction.
What is the basic difference between speed and velocity?
Velocity includes direction.
3|Page
Cartman took a trip South to Saddle River. He reset his odometer at the beginning of the trip. When he
arrived in Saddle River the reading on the odometer was 100 miles. The entire trip took 4 hours. Solve
the following.
1) What total distance did he travel? 100 miles
2) What was his displacement? 100 miles South
3) What was his average speed? 25 miles/hour
4) What was his average velocity? 25 miles/hour South
4|Page
Section 1.3 Speed (pages 17-21)
Speed
d
What is it?
(definition)
s
t
The rate at which position
changes; the distance traveled
divided by the time taken. Refers
to how fast an object is moving and
is always measured in a unit of
distance over a unit of time.
Measurement
Speed
Distance
time
Symbol
s
d
t
Units
Meters/second
Meters
seconds
5|Page
Velocity
d
What is it?
(definition)
v
t
The vector form of speed; a quantity
that specifies both speed and
direction. The rate at which an object
changes its displacement/position and
includes direction.
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
6|Page
Speed & Velocity Examples
1. A football field is about 100 m long. If it takes a person 20 seconds to run its length, how fast
(what speed) were they running?
Looking For
speed
Given
distance = 100 m
time = 20 s
Relationship
s=d/t
Solution
5 m/s
2. Calculate the average speed of a car stuck in traffic that drives 12 kilometers in 2 hours.
Looking For
speed
Given
distance = 12 km
time = 2 hours
Relationship
s=d/t
Solution
6 km/hr
3. A bicyclist travels 60 kilometers in 30 hours South. What is the cyclist’s average velocity?
Looking For
speed
Given
distance = 60 km
time = 30 hrs
Relationship
v=d/t
Solution
2 km/hr South
4. How far will you travel if you run for 600 seconds at 2 m/sec?
Looking For
Distance
Given
Time=600 seconds
Speed = 2 m/s
Relationship
Solution
d=st
1200 meters
5. If we travel a distance of 750 miles in 10 hours, what is the average speed of the trip?
Looking For
speed
Given
distance = 750 miles
time = 10 hours
Relationship
s=d/t
Solution
75 mi/hr
6. Calculate the distance that a person runs if they maintain the average speed of 45 km/hour for 2
hours.
Looking For
Distance
Given
Speed = 45 km/hr
time=2 hours
Relationship
Solution
d=st
90 km
7|Page
7.
Sketch your own example of a situation where a person/object travels with the same average speed and
average velocity.
8.
Sketch your own example of a situation where a person/object travels in two different directions and has
a different displacement and distance.
8|Page
Acceleration
∆v
What is it?
(definition)
a
t
The change of speed over time.
∆v = vf - vi
If an object is
accelerating then it
is either
Changing
speed
Changing
direction
Measurement
acceleration
Change in velocity
time
Symbol
a
∆v
t
Units
meters/second2
meters/second
seconds
9|Page
Acceleration Examples
1. A skater increases her velocity from 2.0 m/s to 10.0 m/s North 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 North.
2. A car accelerates at a rate of 3.0 m/s2 South. 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.
3. While traveling along a highway a driver slows from 24 m/sec to 15 m/sec East in 12 seconds.
What is the automobile’s acceleration?
Looking For
Acceleration
Given
V2=15 m/s
V1=24 m/s
t=12s
Relationship
Solution
-0.75 m/s2 East
4. A parachute on a racing dragster opens and changes the speed of the car from 85 m/sec to 45
m/sec West in a period of 4.5 seconds. What is the acceleration of the dragster?
Looking For
Given
V2=45 m/s
V1=85 m/s
t=4.5s
Relationship
Solution
-8.89 m/s2 West
5. The cheetah, which is the fastest land mammal, can accelerate from 0.0 m/s to 33 m/s East in 3.0
seconds. What is the acceleration of the cheetah?
Looking For
Given
V2=33 m/s
V1=0 m/s
t=3s
Relationship
Solution
11 m/s2East
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6. The Lamborghini Diablo sports car can accelerate from 0.0 m/s to 44 m/s North East in 4.0
seconds. What is the acceleration of this car?
Looking For
Given
V2=44 m/s
V1=0 m/s
t=4s
Relationship
Solution
11 m/s2 North East
7. A helicopter’s speed increases from 25 m/sec to 60 m/sec in 5 seconds. What is the acceleration
of this helicopter?
Looking For
Given
V2=60 m/s
V1=25 m/s
t=5s
Relationship
Solution
7
m/s2 West
8. Which has more acceleration when moving in a straight line – a car increasing its speed from 75
to 90 km/h, or a bicycle that goes from zero to 15 km/h in the same time? Defend your answer.
Acceleration of car
Looking For
Acceleration of car
Given
V2=90 m/s
V1=75 m/s
t=5s
Relationship
Looking For
Acceleration of bike
Given
V2=15 m/s
V1=0 m/s
t=5s
Relationship
3
Solution
m/s2
3
Solution
m/s2
11 | P a g e
d
d
s
t
v
∆v
t
a
t
Class Work
1.
2.
What is the average speed of a cheetah that sprints 100 m East in 4 s?
Looking For
Given
Relationship
Average speed
d=100 m
s=d/t
t=4 s
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
Average speed
d=400 m
s=d/t
=400 m / 25 s = 16 m/s
t=25 s
b. What is the runner’s average velocity?
Looking For
Given
Average velocity
d=0 m
t=25 s
3.
4.
Solution
=100 m / 4 s = 25 m/s
Relationship
v=d/t
Solution
0 m/s
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
Average speed
d=120 m
s=d/t
=120 m / 10 s = 12 m/s
t=10 s
Calculate the average velocity of a car that drives 50 meters North East in 25 seconds.
Looking For
Given
Relationship
Average velocity
d=50 m North
v=d/t
t=25 s
Solution
2 m/s North
5.
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
Time
d=50 m
t=d/v
=50 m/5 m/s
s=5 m/s
=10 s
6.
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
Time
d=5000 m
t=d/v
=5000 m/6 m/s
s=6 m/s
= 833.33 seconds
12 | P a g e
d
d
s
t
v
∆v
t
t
a
Group Work
7.
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
Average speed
d=112 m
s=d/t
=112 m / 4 s = 28 m/s
t=4 s
Looking For
Average velocity
8.
Given
d=112 m south
t=4 s
Relationship
v=d/t
Solution
28 m/s South
Samantha runs a 400 m lap in 53.5 s. What is her average speed? What is her average velocity?
Looking For
Average speed
Given
d=400 m
t=53.5 s
Relationship
s=d/t
Solution
=400 m / 53.5 s = 7.48 m/s
Looking For
Average velocity
Given
d=0 m
t=25 s
Relationship
v=d/t
Solution
0 m/s
9.
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
Average speed
Given
d=300 m
t=3600 s
Relationship
s=d/t
Solution
=300 m / 3600 s = 0.083 m/s
Looking For
Average velocity
Given
d=300 m
t=3600 s
Relationship
s=d/t
Solution
=300 m / 3600 s = 0.083 m/s
North west
10. 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
Time
d=324 m
t=d/v
=324 m / 720 m/s
s=720 m/s
= 0.45 s
13 | P a g e
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
Time
d=18.5 m
t=d/v
0.48 s
s=38.5 m/s
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
Time
d=1000 m
t=d/v
s=850 m/s
3.
Solution
=1.17 s
Every summer Mr. Magoo drives to Michigan. It is 3900 m to get there. If he drives with an averagespeed 100 m/s,
how much time will he spend driving?
Looking For
Given
Relationship
Solution
Time
d=3900 m
t=d/v
=39 s
s=100 m/s
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
Average velocity
d=112 m
s=d/t
=28 m/s
t=4 s
5.
After traveling for 6.0 seconds, a runner reaches a speed of 10 m/s. What is the runner’s
acceleration if they started from rest?
Looking For
Acceleration
Given
V2=10 m/s
V1=0 m/s
t=6s
Relationship
Solution
1.67 m/s2
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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.
First Hallway
Looking For
Given
Relationship
Solution
Time
Distance = 35 m
t=d/v
=10 s
Speed = 3.5 m/s
Second Hallway
Looking For
Time
Given
Distance = 48 m
Speed = 1.2 m/s
Relationship
t=d/v
Solution
=40 s
Given
Distance = 60 m
Speed = 5 m/s
Yes, she gets detention. She arrives 2 seconds late.
Relationship
t=d/v
Solution
=12 s
Final Hallway
Looking For
Time
2.
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?
Tortoise
Looking For
Given
Relationship
Solution
Time
Distance = 1000 m
t=d/v
=5000 s
Speed = 0.2 m/s
Rabbit
First Part
Looking For
Time
Second Part
Looking For
Time
Final Part
Looking For
Time
Given
Distance = 200 m
Speed = 2 m/s
Relationship
t=d/v
Solution
=100 s
Given
Time = 1.3 hrs
Relationship
Solution
=1.3 hours = 4680 s
Given
Relationship
Distance = 800 m
t=d/v
Speed = 3 m/s
Total time for the rabbit = 5047 seconds. The tortoise wins by 47 seconds.
Solution
=266.67 s
15 | P a g e
3.
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?
First Part
Looking For
Given
Relationship
Solution
Time
Distance = 25 m
t=d/v
=2.5 s
Speed = 10 m/s
Second Part
Looking For
Time
Given
Distance = 50 m
Speed = 9.5 m/s
Relationship
Solution
=5.26 s
Given
Distance = 25 m
Speed = 11 m/s
Total time for De La Paz = 10.03 seconds
Relationship
t=d/v
Solution
=2.27 s
Final Part
Looking For
Time
16 | P a g e
Eva recorded the position of a motorized toy car using the origin as her reference point. She wrote this in
the table below. Notice how she labeled the columns using physical quantities that she measured versus
the units used.
a) What patterns do you see in the data?
• As time increases, the position increases.
• Equal time intervals.
• The car travels the same distance per time interval.
b) Explain the meaning of each column in the table. Make sure to specify the difference
between the columns.
• Clock reading refers to the measured time.
• The position refers to how far the car travels from its starting point.
• The time interval is the change in time.
• The change in position is the change in distance between two points.
c) If you were to plot a graph of position vs. time what would you title the graph? Which
variable would you place on the x and y-axes?
Title: Position vs. time
Position (meters)
Clock Reading (seconds)
17 | P a g e
Match the physical quantities with the units from the list below (a quantity can be measured in different
units):
mass, meter, temperature, second, foot, year, centimeter, gram, kilogram, celsius, position, time interval,
hour
Physical Quantity
Possible Units
Temperature
Degrees Celsius
Mass
Gram, kilogram
Position
Meter, centimeter, foot
Time interval
Second, hour, year
Did You Know?
In science, experimenters always put time on the horizontal axis when plotting.
Represent the motion of the ball from Eva’s experiment with a graph. IN
other words, plot the points below on the position-versus-clock reading
graph and draw a trend line. (plot the points on graph 1)
What information can you learn about the motion of the ball from the graph? Explain.
Clock Reading
Position
_____
_____
0
0
1
2
2
4
3
6
4
8
1
2
3
4
18 | P a g e
Graph 1
Now create two additional position-versus-time graphs using the tables below. In the first table Eva
recorded the position of a toy car rolling down a ramp toward her. In the second table Eva recorded the
position of a toy car as it slows to a stop in front of her.
Graph 2
1
2
3
4
19 | P a g e
Clock Reading
t
0s
1s
Position
x
16 cm
23 cm
Time interval
∆t
----1s–0s=1s
2s
28 cm
2s–1s=1s
3s
4s
31 cm
32 cm
3s–2s=1s
4s–3s=1s
Change in position
∆x
----23 cm – 16 cm = 7
cm
28 cm – 23 cm = 5
cm
31 cm – 28 cm = 3 cm
32 cm – 31 cm = 1 cm
Graph 3
1
2
3
4
a)
What are the differences in the motion of the cars for the three experiments Eva
performed?
• Answers will vary
b)
What are the differences between the three graphs? (Specifically comment on what’s
happening to the line.)
• Graph 1 represents a car traveling with constant speed.
• Graph 2 represents a car traveling with increasing speed (speeding up).
• Graph 3 represents a car traveling with decreasing speed (slowing down).
c) Develop a testable hypothesis that relates type of motion to graphical appearance (how
the graph looks).
• Answers will vary.
20 | P a g e
Did You Know?
Position, displacement, distance, and path length: These refer to different things! Position x is the
location of an object relative to a chosen zero on the coordinate axis. Displacement x2 - x1 indicates a
change in position and has a sign indicating the direction of the displacement. The magnitude of that
position change is the distance and is always positive. Path length refers to the total length of the path
that was travelled.
Time: The clock reading or time (t) is the reading on a clock, on a stopwatch, or on some other time
measuring instrument. Time can be measured in many different units, such as seconds, minutes, hours,
days, years, and centuries, etc. In SI system it is measured in seconds.
Time interval: The difference between two clock readings is the time interval. If we represent one time
reading as t1 and another reading as t2 then the time interval between those two clock readings is t2 - t1.
Another way of writing this statement is: Change: The symbol Δ is the Greek letter delta and in physics
and mathematics it reads as delta t (Δt) or the change in t.
Use the graph to record data into the table provided.
Clock Reading
Position
0
1
2
3
4
2
4
6
8
10
Time Interval
Δt
0
1 -0=1
2–1=1
3–2=1
4–3=1
Change in position
Δx
2 – 0 =2
4 – 2 =2
6–4=2
8–6=2
10 – 8 =2
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You should notice that the two physical quantities in the graph did not have units of measure with them.
a) Describe a real life situation for this motion if the units of measure were kilometers and seconds.
b) Describe another situation if the units were centimeters and minutes.
c) Draw a picture for each of the situations you described above.
Hypothesize
Let’s review position versus time graphs. Use what you learned in the previous lesson to help you
develop the following rules.
a) What does constant pace motion look like on a position versus time graph?
• A diagonal line.
b) What does speeding up motion look like on a position versus time graph?
• A line with increasing slope.
c) What does slowing motion look like on a position versus time graph?
• A line with decreasing slope.
Use the graphs and descriptions below to test your rules.
a) This graph represents an object moving at constant pace. Does this match your rule for constant
pace? Explain why or why not. Modify your rule if necessary.
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b) This graph represents a slowing object. Does this match your rule for slowing? Explain why or
why not. Modify your rule if necessary.
c) This graph represents an object speeding up. Does this match your rule for speeding up? Explain
why or why not. Modify your rule if necessary.
23 | P a g e
Examine the graphs below and then answer each of the questions below by recording the associated
letters on the line provided.
a)
Which graphs represent objects moving at constant pace? A
b) Which graphs represents objects speeding up? B, C
c)
Which graphs represent objects that are slowing? D, F
d) Which graphs represent an object moving in the negative direction? A, C, F
e) Do any of the graphs show an object that is not in motion? How do you know? Can we consider
this a constant pace? E
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Use the graph above and calculate the slope of the line for each case. Explain how you calculated the
slope.
Need Some Help?
Slope: Often used to describe the measurement of the steepness of a straight line. A higher slope value
indicates a steeper incline. The slope is defined as the ratio of the change in the value of the dependent
variable (vertical change) over the change in the value of the independent variable (horizontal change).
In other words, vertical change divided by horizontal change!
a) For the skiers, what do you think the slope of the line represents? Try to answer using your
common sense.
•
The slope of the line represents the speed of each skier.
•
Skier 1 speed = 5 m/s
•
Skier 2 speed = 10 m/s
b)What are the units of slope? How do you know?
• Rise/Run or in this case meters/seconds.
c) Refer to the graphs to check if your answer makes sense. How do you know? Is there anything else
you notice? Explain.
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