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Chapter 2
Kinematics: Description of
Motion
Scalars
• A scalar quantity is a quantity that has
magnitude only and has no direction in
space
Examples of Scalar Quantities:
}  Length
}  Area
}  Volume
}  Time
}  Mass
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2.1 Distance and Speed: Scalar
Quantities
Vectors
Distance is the path length traveled from one
location to another. It will vary depending on the
path.
• A vector quantity is a quantity that has
both magnitude and a direction in space
Examples of Vector Quantities:
}  Displacement
}  Velocity
}  Acceleration
}  Force
Distance is a scalar quantity—it is described
only by a magnitude.
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2.1 Distance and Speed: Scalar
Quantities
2.1 Distance and Speed: Scalar
Quantities
Since distance is a scalar, speed is also a scalar
(as is time).
Average speed is the distance traveled divided
by the elapsed time:
Instantaneous speed is the speed measured over
a very short time span.
Question 2.1
Walking the Dog
You and your dog go for a walk to the
park. On the way, your dog takes many
side trips to chase squirrels or examine
fire hydrants. When you arrive at the
park, have you and your dog traveled the
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same distance?
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a) yes
b) no
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2.2 One-Dimensional Displacement and
Velocity: Vector Quantities
A vector has both magnitude
and direction. Manipulating
vectors means defining a
coordinate system, as shown in
the diagrams to the left.
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2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
Displacement is a vector that points from the
initial position to the final position of an
object.
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2.2 One-Dimensional Displacement and
Velocity: Vector Quantities
Note that an object s position coordinate may
be negative, while its velocity may be positive;
the two are independent.
For motion in a straight line with no
reversals, the average speed and the
average velocity are the same.
Otherwise, they are not; indeed, the average
velocity of a round trip is zero, as the total
displacement is zero!
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© 2010 Pearson Education, Inc.
2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
Different ways of visualizing uniform velocity:
This object s velocity
is not uniform. Does it
ever change direction,
or is it just slowing
down and speeding
up?
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2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
Question 2.2
2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
Walking the Dog
You and your dog go for a walk to the
Question 2.2
park. On the way, your dog takes many
Displacement
side trips to chase squirrels or examine
fire hydrants. When you arrive at the
park, do you and your dog have the same
displacement?
a) yes
Does the displacement of an object
a) yes
b) no
depend on the specific location of
b) no
the origin of the coordinate system?
c) it depends on the
coordinate system
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2.3 Acceleration
Question 2.2
Acceleration is the rate at which velocity
changes.
Velocity in One Dimension
If the average velocity is non-zero over
some time interval, does this mean that
the instantaneous velocity is never zero
during the same interval?
a) yes
b) no
c) it depends
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2.3 Acceleration
2.3 Acceleration
Acceleration means that the speed of an object
is changing, or its direction is, or both.
Acceleration may result in an
object either speeding up or
slowing down (or simply
changing its direction).
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2.3 Acceleration
If the acceleration is constant, we can find the
velocity as a function of time:
Question 2.3
Position and Speed
a) yes
If the position of a car is
zero, does its speed have to
be zero?
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b) no
c) it depends on
the position
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2.4 Kinematic Equations
(Constant Acceleration)
From previous sections:
Question 2.4
You drive for 30 minutes at 30 mi/
a) more than 40 mi/hr
hr and then for another 30
b) equal to 40 mi/hr
minutes at 50 mi/hr. What is your
average speed for the whole trip?
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Cruising Along I
c) less than 40 mi/hr
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2.4 Kinematic Equations
(Constant Acceleration)
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2.4 Kinematic Equations
(Constant Acceleration)
These are all the equations we have derived for
constant acceleration. The correct equation for a
problem should be selected considering the
information given and the desired result.
Substitution gives:
and:
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Vector Diagrams
•  Vector diagrams are
diagrams which use
vector arrows to
depict the direction
and relative
magnitude of a vector
quantity.
Vector Diagrams
•  Vector diagrams can
be used to describe
the velocity of a
moving object during
its motion.
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Describing Motion with
Position vs. Time
Graphs
The Meaning of Shape
for a p-t Graph
Constant Velocity
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•  To begin, consider a
car moving with a
constant, rightward
(+) velocity - say of
+10 m/s.
•  Note that a motion
described as a
constant, positive
velocity results in a
line of constant and
positive slope when
plotted as a positiontime graph.
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The position vs. time graphs for the two types of motion - constant
velocity and changing velocity (acceleration) - are depicted as follows.
Changing Velocity
•  Now consider a car moving with a rightward (+),
changing velocity (acceleration) - that is, a car
that is moving rightward but speeding up or
accelerating
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Constant Velocity
Positive Velocity
Positive Velocity
Changing Velocity (acceleration)
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Importance of slope
•  If the velocity is constant, then the slope is
constant (i.e., a straight line).
•  If the velocity is changing, then the slope is
changing (i.e., a curved line).
•  If the velocity is positive, then the slope is
positive (i.e., moving upwards and to the
right).
Slope of p vs t
Slow, Rightward (+)
Constant Velocity
Fast, Rightward (+)
Constant Velocity
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Slope
Meaning of slope
Slow, Leftward (-)
Constant Velocity
Fast, Leftward (-)
Constant Velocity
Negative (-) Velocity Leftward (-)
Slow to Fast
Fast to Slow
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Determining the Slope on a p-t Graph
•  The slope of the line is +10 meter/1 second. It is obvious
that in this case the slope of the line (10 m/s) is the same
as the velocity of the car
•  In this part of the lesson, we will examine
how the actual slope value of any straight
line on a graph is the velocity of the object.
•  Consider a car moving with a constant
velocity of +10 m/s for 5 seconds. The
next diagram depicts such a motion.
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•  Now consider a car moving at a constant
velocity of +5 m/s for 5 seconds, abruptly
stopping, and then remaining at rest (v = 0
m/s) for 5 seconds.
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Check your understanding
Determining the slope
•  The line is sloping upwards to the right. But
mathematically, by how much does it slope
upwards per 1 second along the horizontal
(time) axis? To answer this question we must
use the slope equation.
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The Meaning of Shape for a v-t Graph
•  Consider a car moving with a constant,
rightward (+) velocity - say of +10 m/s.
As learned in an earlier lesson, a car
moving with a constant velocity is a car
with zero acceleration.
•  Answer: -3.0 m/s
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•  Note that a motion described as a constant,
positive velocity results in a line of zero slope (a
horizontal line has zero slope) when plotted as
a velocity-time graph. Furthermore, only
positive velocity values are plotted,
corresponding to a motion with positive velocity.
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•  Now consider a car moving with a
rightward (+), changing velocity - that is,
a car that is moving rightward but
speeding up or accelerating.
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Notice that the slope of a velocity-time graph
represents the acceleration of the object
•  The velocity vs. time graphs for the two
types of motion - constant velocity and
changing velocity (acceleration) - can be
summarized as follows
Positive Velocity
Zero Acceleration
Positive Velocity
Positive Acceleration
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•  Now how can one tell if the object is speeding
up or slowing down? Speeding up means that
the magnitude (the value) of the velocity is
getting large
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Question 2.5
Question 2.5
Throwing Rocks I
You drop a rock off a
a) the separation increases as they fall
bridge. When the rock
has fallen 4 m, you drop a b) the separation stays constant at 4 m
c) the separation decreases as they fall
second rock. As the two
rocks continue to fall,
d) it is impossible to answer without more
what happens to their
information
separation?
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Throwing Rocks II
You drop a rock off a
a) both increase at the same rate
bridge. When the rock
b) the velocity of the first rock increases
has fallen 4 m, you drop
faster than the velocity of the second
a second rock. As the
c)
the velocity of the second rock
two rocks continue to
increases faster than the velocity of the
fall, what happens to
first
their velocities?
d) both velocities stay constant
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