PHYSICS
Principles and Problems
Chapter 2: Representing Motion
CHAPTER
2
Representing Motion
BIG IDEA
You can use displacement and velocity to describe
an object’s motion.
CHAPTER
2
Table Of Contents
Section 2.1
Picturing Motion
Section 2.2
Where and When?
Section 2.3
Position-Time Graphs
Section 2.4
How Fast?
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SECTION
Picturing Motion
2.1
MAIN IDEA
You can use motion diagrams to show how an object’s
position changes over time.
Essential Questions
•
How do motion diagrams represent motion?
•
How can you use a particle model to represent a moving
object?
SECTION
Picturing Motion
2.1
Review Vocabulary
• Model a representation of an idea, event, structure or
object to help people better understand it.
New Vocabulary
• Motion diagram
• Particle model
SECTION
2.1
Picturing Motion
All Kinds of Motion
• Perceiving motion is instinctive—your eyes pay
more attention to moving objects than to
stationary ones. Movement is all around you.
• Movement travels in many directions, such as the
straight-line path of a bowling ball in a lane’s
gutter, the curved path of a tether ball, the spiral of
a falling kite, and the swirls of water circling a
drain.
SECTION
2.1
Picturing Motion
All Kinds of Motion (cont.)
• When an object is in motion, its position changes.
Its position can change along the path of a
straight line, a circle, an arc, or a back-and-forth
vibration.
SECTION
2.1
Picturing Motion
All Kinds of Motion (cont.)
• Straight-line motion follows a path directly
between two points without turning left or right.
–Ex. Forward and backward, up and down, or north and
south.
• A description of motion relates to place and time.
You must be able to answer the questions of
where and when an object is positioned to
describe its motion.
SECTION
2.1
Picturing Motion
Motion Diagrams
Click image to view movie.
SECTION
2.1
Section Check
Explain how applying the particle model
produces a simplified version of a motion
diagram?
SECTION
2.1
Section Check
Answer
Answer: Keeping track of the motion of the runner is
easier if we disregard the movements of the arms and
the legs, and instead concentrate on a single point at
the center of the body. In effect, we can disregard the
fact that the runner has some size and imagine that
the runner is a very small object located precisely at
that central point. A particle model is a simplified
version of a motion diagram in which the object in
motion is replaced by a series of single points.
SECTION
2.1
Section Check
Which statement describes best the motion
diagram of an object in motion?
A. a graph of the time data on a horizontal axis and the
position on a vertical axis
B. a series of images showing the positions of a moving
object at equal time intervals
C. a diagram in which the object in motion is replaced by a
series of single points
D. a diagram that tells us the location of the zero point of
the object in motion and the direction in which the object
is moving
SECTION
2.1
Section Check
Answer
Reason: A series of images showing the positions
of a moving object at equal time intervals
is called a motion diagram.
SECTION
2.1
Section Check
What is the purpose of drawing a motion
diagram or a particle model?
A. to calculate the speed of the object in motion
B. to calculate the distance covered by the object in a
particular time
C. to check whether an object is in motion
D. to calculate the instantaneous velocity of the object
in motion
SECTION
2.1
Section Check
Answer
Reason: In a motion diagram or a particle model,
we relate the motion of the object with the
background, which indicates that relative
to the background, only the object is in
motion.
SECTION
Where and When?
2.2
MAIN IDEA
A coordinate system is helpful when you are describing motion.
Essential Questions
•
What is a coordinate system?
•
How does the chosen coordinate system affect the sign of
objects’ positions?
•
How are time intervals measured?
•
What is displacement?
•
How are motion diagrams helpful in answering questions
about an object’s position or displacement?
SECTION
Where and When?
2.2
Review Vocabulary
• Dimension extension in a given direction;one
dimension is along a straight line; three dimensions are
height, width and length.
New Vocabulary
• Coordinate system
• Vector
• Origin
• Scalar
• Position
• Time interval
• Distance
• Displacement
• Magnitude
• Resultant
SECTION
2.2
Where and When?
Coordinate Systems
• A coordinate system tells you the location of the
zero point of the variable you are studying and
the direction in which the values of the variable
increase.
• The origin is the point at which both variables
have the value zero.
SECTION
2.2
Where and When?
Coordinate Systems (cont.)
• In the example of the runner, the origin,
represented by the zero end of the measuring
tape, could be placed 5 m to the left of the tree.
SECTION
2.2
Where and When?
Coordinate Systems (cont.)
• The motion is in a straight line, thus, your measuring
tape should lie along that straight line. The straight
line is an axis of the coordinate system.
SECTION
2.2
Where and When?
Coordinate Systems (cont.)
• You can indicate how far away an object is from the origin
at a particular time on the simplified motion diagram by
drawing an arrow from the origin to the point representing
the object, as shown in the figure.
SECTION
2.2
Where and When?
Coordinate Systems (cont.)
• The two arrows locate the runner’s position at two
different times.
• Because the motion in the figure below is in one direction,
the arrow lengths represent distance.
SECTION
2.2
Where and When?
Coordinate Systems (cont.)
• The length of how far an object is from the origin
indicates its distance from the origin.
SECTION
2.2
Where and When?
Coordinate Systems (cont.)
• A position 9 m to the left of the tree, 5 m left of the
origin, would be a negative position, as shown in
the figure below.
SECTION
2.2
Where and When?
Vectors and Scalars
• Quantities that have both size, also called
magnitude, and direction, are called vectors, and
can be represented by arrows.
– Vector quantities will be represented by boldface
letters.
• Quantities that are just numbers without any direction,
such as distance, time, or temperature, are called
scalars.
– Scalars quantities will be represented by regular
letters.
SECTION
2.2
Where and When?
Vectors and Scalars (cont.)
• The difference between the initial and the final
times is called the time interval.
SECTION
2.2
Where and When?
Vectors and Scalars (cont.)
• The common symbol for a time interval is ∆t,
where the Greek letter delta, ∆, is used to
represent a change in a quantity.
SECTION
2.2
Where and When?
Vectors and Scalars (cont.)
• The time interval is defined mathematically as
follows:
• Although i and f are used to represent the initial
and final times, they can be initial and final times
of any time interval you choose.
• The time interval is a scalar because it has no
direction.
SECTION
2.2
Where and When?
Vectors and Scalars (cont.)
• The figure below shows the position of the runner at
both the tree and the lamppost.
• These arrows have magnitude and direction.
• Position is a vector with the arrow’s tail at the origin
and the arrow’s tip at the place.
SECTION
2.2
Where and When?
Vectors and Scalars (cont.)
• The symbol x is used to represent position vectors
mathematically.
• Xi represents the position at the tree, xf represents the
position at the lamppost and ∆x, represents the change in
position, displacement, from the tree to the lamppost.
SECTION
2.2
Where and When?
Vectors and Scalars (cont.)
• Displacement is defined mathematically as:
∆x = xf - xi
• Remember that the initial and final positions are
the start and end of any interval you choose, so
a plus and minus sign might be used to indicate
direction.
SECTION
2.2
Where and When?
Vectors and Scalars (cont.)
• A vector that
represents the
sum o f two other
vectors is called
a resultant.
• The figure to the
right shows how
to add and
subtract vectors
in one
dimension.
SECTION
2.2
Where and When?
Vectors and Scalars (cont.)
• To completely describe an object’s displacement, you
must indicate the distance it traveled and the direction it
moved. Thus, displacement, a vector, is not identical to
distance, a scalar; it is distance and direction.
• While the vectors drawn to represent each position
change, the length and direction of the displacement
vector does not.
• The displacement vector is always drawn with its flat end,
or tail, at the earlier position, and its point, or tip, at the
later position.
SECTION
2.2
Section Check
Differentiate between scalar and vector
quantities.
SECTION
2.2
Section Check
Answer
Reason: Quantities that have both magnitude and
direction are called vectors, and can be
represented by arrows. Quantities that are just
numbers without any direction, such as time, are
called scalars.
SECTION
Section Check
2.2
What is displacement?
A. the vector drawn from the initial position to the final
position of the motion in a coordinate system
B. the distance between the initial position and the final
position of the motion in a coordinate system
C. the amount by which the object is displaced from the
initial position
D. the amount by which the object moved from the initial
position
SECTION
2.2
Section Check
Answer
Reason: Options B, C, and D are all defining the
distance of the motion and not the
displacement. Displacement is a vector
drawn from the starting position to the final
position.
SECTION
2.2
Section Check
Refer to the adjoining figure and calculate the
time taken by the car to travel from one signal to
another signal?
A. 20 min
C. 25 min
B. 45 min
D. 5 min
SECTION
2.2
Section Check
Answer
Reason: Time interval t = tf – ti
Here tf = 01:45 and ti = 01:20
Therefore, t = 25 min
SECTION
Position-Time Graphs
2.3
MAIN IDEA
You can use position-time graphs to determine an object’s
position at a certain time.
Essential Questions
•
What information do position-time graphs provide?
•
How can you use a position-time graph to interpret an
object’s position or displacement?
•
What are the purposes of equivalent representations of
an object’s motion?
SECTION
2.3
Position-Time Graphs
Review Vocabulary
• Intersection a point where lines meet and cross.
New Vocabulary
• Position-time graph
• Instantaneous position
SECTION
2.3
Position-Time Graphs
Finding Positions
Click image to view movie.
SECTION
2.3
Position-Time Graphs
Finding Positions (cont.)
• Graphs of an object’s position and time contain
useful information about an object’s position at
various times. It can be helpful in determining the
displacement of an object during various time
intervals.
SECTION
2.3
Position-Time Graphs
Finding Positions (cont.)
• The data in the table can
be presented by plotting
the time data on a
horizontal axis and the
position data on a
vertical axis, which is
called a position-time
graph.
SECTION
2.3
Position-Time Graphs
Finding Positions (cont.)
• To draw the graph, plot the object’s recorded positions.
Then, draw a line that best fits the recorded points. This
line represents the most likely positions of the runner at
the times between the recorded data points.
• The symbol x represents the
instantaneous position of the
object—the position at a
particular instant.
SECTION
2.3
Position-Time Graphs
Finding Positions (cont.)
• Words, pictorial representations, motion diagrams,
data tables, and position-time graphs are all
representations that are equivalent. They all
contain the same information about an object’s
motion.
• Depending on what you want to find out about an
object’s motion, some of the representations will
be more useful than others.
SECTION
2.3
Position-Time Graphs
Multiple Objects on a Position-Time Graph
In the graph, when and
where does runner B
pass runner A?
SECTION
2.3
Position-Time Graphs
Multiple Objects on a Position-Time
Graph (cont.)
Step 1: Analyze the Problem
Restate the questions.
Question 1: At what time do A and B have the
same position?
Question 2: What is the position of runner A and
runner B at this time?
SECTION
2.3
Position-Time Graphs
Multiple Objects on a Position-Time
Graph (cont.)
Step 2: Solve for the Unknown
SECTION
2.3
Position-Time Graphs
Multiple Objects on a Position-Time
Graph (cont.)
Question 1
In the figure, examine the
graph to find the intersection
of the line representing the
motion of A with the line
representing the motion of B.
These lines intersect at 45 s.
SECTION
2.3
Position-Time Graphs
Multiple Objects on a Position-Time
Graph (cont.)
Question 2
In the figure, examine the
graph to find the intersection
of the line representing the
motion of A with the line
representing the motion of B.
The position of both runners
is about 190m from the origin.
SECTION
2.3
Position-Time Graphs
Multiple Objects on a Position-Time
Graph (cont.)
B passes A about 190 m
beyond the origin, 45.0 s
after A has passed the
origin.
SECTION
2.3
Position-Time Graphs
Considering the Motion of Multiple Objects
The steps covered were:
Step 1: Analyze the Problem
Restate the questions.
Step 2: Solve for the Unknown
SECTION
2.3
Section Check
A position-time graph of an athlete winning the
100-m run is shown. Estimate the time taken by
the athlete to reach 65 m.
A. 6.0 s
B. 6.5 s
C. 5.5 s
D. 7.0 s
SECTION
2.3
Section Check
Answer
Reason: Draw a horizontal line
from the position of 65 m to the
line of best fit. Draw a vertical
line to touch the time axis from
the point of intersection of the
horizontal line and line of best fit.
Note the time where the vertical
line crosses the time axis. This is
the estimated time taken by the
athlete to reach 65 m.
SECTION
2.3
Section Check
A position-time graph of an athlete winning the
100-m run is shown. What was the
instantaneous position of the athlete at 2.5 s?
A. 15 m
B. 20 m
C. 25 m
D. 30 m
SECTION
2.3
Section Check
Answer
Reason: Draw a vertical line
from the position of 2.5 m to the
line of best fit. Draw a horizontal
line to touch the position axis
from the point of intersection of
the vertical line and line of best
fit. Note the position where the
horizontal line crosses the
position axis. This is the
instantaneous position of the
athlete at 2.5 s.
SECTION
2.3
Section Check
From the following
position-time graph of
two brothers running a
100-m dash, at what time
do both brothers have
the same position? The
smaller brother started
the race from the 20-m
mark.
SECTION
2.3
Section Check
Answer
Reason: The two brothers meet at 6 s. In the figure,
we find the intersection of lines representing the
motion of one brother with the line representing the
motion of other brother. These lines intersect at 6 s
and at 60 m.
SECTION
How Fast?
2.4
MAIN IDEA
An object’s velocity is the rate of change in its position.
Essential Questions
•
What is velocity?
•
What is the difference between speed and velocity?
•
How can you determine an object’s average velocity
from a position-time graph?
•
How can you represent motion with pictorial, physical,
and mathematical models?
SECTION
How Fast?
2.4
Review Vocabulary
• Absolute value magnitude of a number, regardless of
sign.
New Vocabulary
• Average velocity
• Average speed
• Instantaneous velocity
SECTION
2.4
How Fast?
Velocity and Speed
• Suppose you recorded two joggers in one motion diagram,
as shown in the figure below. The position of the jogger
wearing red changes more than the of the jogger wearing
blue
• For a fixed time, the
magnitude of the
displacement (∆x), is
greater for the jogger in
red.
• If each jogger travels 100m, the time interval (∆t) would
be smaller for the jogger in red.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• Recall from Chapter 1 that to find the slope, you first
choose two points on the line.
• Next, you subtract the vertical coordinate (x in this case) of
the first point from the vertical coordinate of the second
point to obtain the rise of the line.
• After that, you subtract the horizontal coordinate (t in this
case) of the first point from the horizontal coordinate of the
second point to obtain the run.
• Finally, you divide the rise by the run to obtain the slope.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• The slopes of the two lines are found as follows:
• A greater
slope,
shows that
the red
jogger
traveled
faster.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• The unit of the slope is meters per second. In
other words, the slope tells how many meters the
runner moved in 1 s.
• The slope is the change in position, divided by the
time interval during which that change took place,
or (xf - xi) / (tf - ti), or Δx/Δt.
• When Δx gets larger, the slope gets larger; when
Δt gets larger, the slope gets smaller.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• The slope of a position-time graph for an object is
the object’s average velocity and is represented
by the ratio of the change of position to the time
interval during which the change occurred.
Average Velocity
≡
Δx
_______
Δt
(xf - xi)
= ________
(tf - ti)
• The symbol ≡ means that the left-hand side of the
equation is defined by the right-hand side.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• It is a common
misconception to say that
the slope of a positiontime graph gives the
speed of the object.
• The slope of the positiontime graph on the right is
–5.0 m/s. It indicates the
average velocity of the
object and not its speed.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• The object moves in
the negative direction
at a rate of 5.0 m/s.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• The slope’s absolute
value is the object’s
average speed,
5.0m/s, which is the
distance traveled
divided by the time
taken to travel that
distance.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• If an object moves in the negative direction, then
its displacement is negative. The object’s velocity
will always have the same sign as the object’s
displacement.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
The graph describes the
motion of a student
riding his skateboard
along a smooth,
pedestrian-free
sidewalk. What is his
average velocity? What
is his average speed?
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
Step 1: Analyze and Sketch the Problem
Identify the coordinate system of the graph.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
Step 2: Solve for the Unknown
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
Identify the unknown variables.
Unknown:
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
Find the average velocity using two points on the
line.
Use magnitudes with signs indicating directions.
Δx
= _____
Δt
(xf - xi)
= ______
(tf - ti)
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
Substitute x2 = 12.0 m, x1 = 6.0 m, t2 = 8.0 s,
t1 = 4.0 s:
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
Step 3: Evaluate the Answer
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
Are the units correct?
m/s are the units for both velocity and speed.
Do the signs make sense?
The positive sign for the velocity agrees with
the coordinate system. No direction is
associated with speed.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
The steps covered were:
Step 1: Analyze and Sketch the Problem
Identify the coordinate system of the graph.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
The steps covered were:
Step 2: Solve for the Unknown
Find the average velocity using two points on the
line.
The average speed is the absolute value of the
average velocity.
Step 3: Evaluate the Answer
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• A motion diagram shows the position of a moving object at
the beginning and end of a time interval. During that time
interval, the speed of the object could have remained the
same, increased, or decreased. All that can be determined
from the motion diagram is the average velocity.
• The speed and direction of an object at a particular instant
is called the instantaneous velocity.
• The term velocity refers to instantaneous velocity and is
represented by the symbol v.
SECTION
2.4
How Fast?
Velocity and Speed (cont.)
• Although the average velocity is in the same direction
as displacement, the two quantities are not measured
in the same units.
• Nevertheless, they are proportional—when
displacement is greater during a given time interval,
so is the average velocity.
• A motion diagram is not a precise graph of average
velocity, but you can indicate the direction and
magnitude of the average velocity on it.
SECTION
2.4
How Fast?
Equation of Motion
• Using the position-time graph
used before with a slope of
-5.0m/s, remember that you
can represent any straight line
with the equation, y = mx + b.
• y is the quantity plotted on the
vertical axis, m is the line’s
slope, x is the quantity plotted
on the horizontal axis and b is
the line’s y-intercept.
SECTION
2.4
How Fast?
Equation of Motion (cont.)
• Based on the information shown in
the table, the equation y = mx + b
becomes x = t + xi, or, by inserting
the values of the constants,
x = (–5.0 m/s)t + 20.0 m.
• You cannot set two items with
different units equal to each
other in an equation.
Comparison of Straight
Lines with Position-Time
Graphs
General
Variable
Specific
Motion
Variable
y
x
m
Value in
Graph
-5.0m/s
x
t
b
xi
20.0m
SECTION
2.4
How Fast?
Equation of Motion (cont.)
• An object’s position is equal to the average
velocity multiplied by time plus the initial position.
• This equation gives you another way to represent
the motion of an object.
SECTION
2.4
Section Check
Which of the following statements defines the
velocity of the object’s motion?
A. the ratio of the distance covered by an object to the
respective time interval
B. the rate at which distance is covered
C. the distance moved by a moving body in unit time
D. the ratio of the displacement of an object to the
respective time interval
SECTION
2.4
Section Check
Answer
Reason: Options A, B, and C define the speed of
the object’s motion. The velocity of a
moving object is defined as the ratio of the
displacement (x) to the time interval (t).
SECTION
2.4
Section Check
Which of the statements given below is correct?
A. Average velocity cannot have a negative value.
B. Average velocity is a scalar quantity.
C. Average velocity is a vector quantity.
D. Average velocity is the absolute value of the
slope of a position-time graph.
SECTION
2.4
Section Check
Answer
Reason: Average velocity is a vector quantity,
whereas all other statements are true for
scalar quantities.
SECTION
2.4
Section Check
The position-time graph of a car moving on a
street is given here. What is the average
velocity of the car?
A. 2.5 m/s
B. 5 m/s
C. 2 m/s
D. 10 m/s
SECTION
2.4
Section Check
Answer
Reason: The average velocity of an object is the
slope of a position-time graph.
CHAPTER
Representing Motion
2
Resources
Physics Online
Study Guide
Chapter Assessment Questions
Standardized Test Practice
SECTION
Picturing Motion
2.1
Study Guide
• A motion diagram shows the position of an object
at successive equal time intervals.
• In the particle model motion diagram, an object’s
position at successive times is represented by a
series of dots. The spacing between dots
indicates whether the object is moving faster or
slower.
SECTION
Where and When?
2.2
Study Guide
• A coordinate system gives the location of the
zero point of the variable you are studying and
the direction in which the values of the variable
increase.
• A vector drawn from the origin of a coordinate
system to an object indicates the object’s
position in that coordinate system. The
directions chosen as positive and negative on
the coordinate system.
SECTION
Where and When?
2.2
Study Guide
• A time interval is the difference between two
times.
• Change in position is displacement, which has
both magnitude and direction.
SECTION
Where and When?
2.2
Study Guide
• On a motion diagram, the displacement vector’s
length represents how far the object was
displaced. The vector points in the direction of
the displacement, from xi to xf.
SECTION
Position-Time Graphs
2.3
Study Guide
• Position-time graphs provide information about
the motion of objects. They also might indicate
where and when two objects meet.
• The line on a position-time graph describes an
object’s position at each time.
• Motion can be described using words, motion
diagrams, data tables or graphs.
SECTION
How Fast?
2.4
Study Guide
• An object’s velocity tells how fast it is moving and
in what direction it is moving.
• Speed is the magnitude of velocity.
• Slope on a position-time graph described the
average velocity of the object.
SECTION
How Fast?
2.4
Study Guide
• You can represent motion with pictures and
physical models. A simple equation relates an
object’s initial position (xi), its constant average
velocity,
its position (x) and the time (t) since
the object was at its initial position.
CHAPTER
2
Representing Motion
Chapter Assessment
What should be true about the motion of an object in
order for you to treat that object as if it were a particle?
A. The object should be no smaller than your fist.
B. The object should be small compared to its motion.
C. The object should be no larger than you can lift.
D. The object should not be moving faster than the speed
of sound.
CHAPTER
2
Representing Motion
Chapter Assessment
Reason: you can treat even planets and stars as
particles as long as those objects are small
compared to the motion you are studying.
CHAPTER
2
Representing Motion
Chapter Assessment
Which is the distance and direction from one
point to another?
A. Displacement
B. Magnitude of distance
C. Position
D. Velocity
CHAPTER
2
Representing Motion
Chapter Assessment
Reason: Velocity is speed and direction.
CHAPTER
2
Representing Motion
Chapter Assessment
On a position-time graph, how would you indicate that
object A has a greater velocity than object B?
A. Make the slope for object A less than the slope for object
B.
B. Make the slope for object A greater than the slope for
object B.
C. Make the y-intercept for object A less then the y-intercept
for object B.
D. Make the y-intercept for object A greater than the yintercept for object B.
CHAPTER
2
Representing Motion
Chapter Assessment
Answer: The slope of a line on a position-time
graph indicates the object’s velocity.
CHAPTER
2
Representing Motion
Chapter Assessment
A car is moving at a constant speed of 25 m/s. How far
does this car move in 0.2 s, the approximate reaction
time for an average person?
A. 5 m
B. 10 m
C. 25 m
D. 50 m
CHAPTER
2
Representing Motion
Chapter Assessment
Reason: (25m/s)(0.2s) = 5m
CHAPTER
2
Representing Motion
Chapter Assessment
Which is a measurement of velocity?
A. 20 m
B. 33 km/s
C. 300 km west
D. 7800 m/s north
CHAPTER
2
Representing Motion
Chapter Assessment
Reason: Velocity measures both speed and
direction.
CHAPTER
Representing Motion
2
Standardized Test Practice
Which statement about velocity vectors is true?
A. All velocity vectors are positive.
B. Velocity vectors have magnitude but no direction.
C. Velocity vectors and displacement vectors are the
same thing.
D. A velocity vector’s length should be proportional to
the object’s speed.
CHAPTER
2
Representing Motion
Standardized Test Practice
What is the average speed of a sprinter who
completes a 55-m dash in 6.2 s?
A. 6.2 m/s
B. 7.1 m/s
C. 8.9 m/s
D. 11 m/s
CHAPTER
2
Representing Motion
Standardized Test Practice
Car A is moving faster than Car B on the highway. Which
statement describes the particle model motion diagrams
for Car A and Car B?
A. The does for Car A are farther apart than the dots for Car B.
B. The dots for Car A are closer together than the dots for Car B.
C. The slope of the motion diagram is greater for Car A than for
Car B.
D. The slope of the motion diagram is less for Car A than for Car
B.
CHAPTER
2
Representing Motion
Standardized Test Practice
An athlete runs four complete laps around a 200-m
track. What is the athlete’s displacement?
A. 0 m
B. 200 m
C. 400 m
D. 800 m
CHAPTER
2
Representing Motion
Standardized Test Practice
Which correctly describes a relationship between an
object’s particle model motion diagram and that object’s
graph of position v. time?
A. If the dots on the motion diagram are closer together, then the
slope of the graph is greater.
B. If the dots on the motion diagram are farther apart, then the
slope of the graph is greater.
C. If the dots on the motion diagram are closer together, then the
y-intercept of the graph is less.
D. If the dots on the motion diagram are farther apart, then the yintercept of the graph is less.
CHAPTER
2
Representing Motion
Standardized Test Practice
Test-Taking Tip
Stock up on Supplies
Bring all your test-taking tools: number two pencils,
black and blue pens, erasers, correction fluid, a
sharpener, a ruler, a calculator, and a protractor.
CHAPTER
2
Representing Motion
Chapter Resources
Coordinate Systems
CHAPTER
2
Representing Motion
Chapter Resources
Coordinate Systems Showing Position
CHAPTER
2
Representing Motion
Chapter Resources
Motion Diagram Showing Negative
Position
CHAPTER
2
Representing Motion
Chapter Resources
Position-Time Graph for the Runner
End of Custom Shows