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•
The kinematics of motion in
one dimension
•
Problem

solving strategies
•
Free fall
Chapter 2
Motion in One Dimension
Topics:
Sample question:
Horses can run much much faster than humans, but if the length of
the course is right, a human can beat a horse in a race. When, and
why, can a man outrun a horse?
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From this class:
•
In Chapter 1 you began studying motion in one dimension. We
continue the development of the concepts in this chapter.
•
In Chapter 1 you saw how to represent motion using a motion
diagram. In this chapter we will look at other ways to represent
motion.
From previous classes:
•
We will use graphical representations of motion extensively in
this chapter. You should have learned how to draw, interpret, and
work with graphs in previous courses.
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Looking Back: What You Already Know
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Reading Quiz
1.
The slope at a point on a position

versus

time graph of an
object is
A.
the object’s speed at that point.
B.
the object’s average velocity at that point.
C.
the object’s instantaneous velocity at that point.
D.
the object’s acceleration at that point.
E.
the distance traveled by the object to that point.
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1.
The slope at a point on a position

versus

time graph of an
object is
C.
the object’s instantaneous velocity at that point.
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Answer
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Reading Quiz
2.
The area under a velocity

versus

time graph of an object is
A.
the object’s speed at that point.
B.
the object’s acceleration at that point.
C.
the distance traveled by the object.
D.
the displacement of the object.
E.
This topic was not covered in this chapter.
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2.
The area under a velocity

versus

time graph of an object is
D.
the displacement of the object.
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Answer
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Reading Quiz
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3.
A 1

pound ball and a 100

pound ball are dropped from a height
of 10 feet at the same time. In the absence of air resistance
A.
the 1

pound ball hits the ground first.
B.
the 100

pound ball hits the ground first.
C.
the two balls hit the ground at the same time.
D.
There’s not enough information to determine which ball wins
the race.
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3.
A 1

pound ball and a 100

pound ball are dropped from a height
of 10 feet at the same time. In the absence of air resistance
C.
the two balls hit the ground at the same time.
Answer
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Representations
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Motion diagram (student walking to school)
Table of data
Graph
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Solving Problems
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Solving Problems (continued)
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Interpreting Graphs
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Here is a motion diagram of a car moving along a straight stretch of
road:
Which of the following velocity

versus

time graphs matches this
motion diagram?
Checking Understanding
A.
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B.
C.
D.
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Here is a motion diagram of a car moving along a straight stretch of
road:
Which of the following velocity

versus

time graphs matches this
motion diagram?
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C.
Answer
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Checking Understanding
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A graph of position versus time for a
basketball player moving down the
court appears like so:
Which of the following velocity graphs matches the above position
graph?
A.
B.
C.
D.
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A graph of position versus time for a
basketball player moving down the
court appears like so:
Which of the following velocity graphs matches the above position
graph?
C.
Answer
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A graph of velocity versus time for a
hockey puck shot into a goal appears
like so:
Which of the following position graphs matches the above velocity
graph?
Checking Understanding
A.
B.
C.
D.
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A graph of velocity versus time for a
hockey puck shot into a goal appears
like so:
Which of the following position graphs matches the above velocity
graph?
D.
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Answer
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Examples
A soccer player is 15 m from her opponent’s goal. She kicks the
ball hard; after 0.50 s, it flies past a defender who stands 5 m
away, and continues toward the goal. How much time does the
goalie have to move into position to block the kick from the
moment the ball leaves the kicker’s foot?
Cleveland and Chicago are 340 miles apart by train. Train A
leaves Cleveland going west to Chicago at 1:00 PM, traveling at
60 mph. Train B leaves Chicago going east to Cleveland at 2:00
PM, going 45 mph. At what time do the two trains meet? How far
are they from Chicago at this time?
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Acceleration
Acceleration is:
•
The rate of change of
velocity
•
The slope of a velocity

versus

time graph
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These four motion diagrams show the motion of a particle along
the
x

axis. Rank these motion diagrams by the magnitude of the
acceleration. There may be ties.
Checking Understanding
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These four motion diagrams show the motion of a particle along the
x

axis. Which motion diagrams correspond to a positive
acceleration? Which motion diagrams correspond to a negative
acceleration?
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Checking Understanding
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These six motion diagrams show the motion of a particle along the
x

axis. Rank the accelerations corresponding to these motion
diagrams, from most positive to most negative. There may be ties.
Checking Understanding
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Dinner at a Distance, Part I
Chameleons catch insects with their tongues, which they can
extend to great lengths at great speeds. A chameleon is aiming for
an insect at a distance of 18 cm. The insect will sense the attack
and move away 50 ms after it begins. In the first 50 ms, the
chameleon’s tongue accelerates at 250 m/s
2
for 20 ms, then travels
at constant speed for the remaining 30 ms. Does its tongue reach
the 18 cm extension needed to catch the insect during this time?
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Dinner at a Distance, Part II
Cheetahs can run at incredible speeds, but they can’t keep up
these speeds for long. Suppose a cheetah has spotted a gazelle.
In five long strides, the cheetah has reached its top speed of 27
m/s. At this instant, the gazelle, at a distance of 140 m from the
running cheetah, notices the danger and heads directly away. The
gazelle accelerates at 7.0 m/s² for 3.0 s, then continues running
at a constant speed that is much less than the cheetah’s speed.
But the cheetah can only keep running for 15 s before it must
break off the chase. Does the cheetah catch the gazelle, or does
the gazelle escape?
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Free Fall
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An arrow is launched vertically upward. It
moves straight up to a maximum height, then
falls to the ground. The trajectory of the
arrow is noted. At which point of the
trajectory is the arrow’s acceleration the
greatest? The least? Ignore air resistance;
the only force acting is gravity.
Checking Understanding
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An arrow is launched vertically upward. It moves straight up to a
maximum height, then falls to the ground. The trajectory of the arrow
is noted. Which graph best represents the vertical velocity of the
arrow as a function of time? Ignore air resistance; the only force
acting is gravity.
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Checking Understanding
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An arrow is launched vertically upward. It moves straight up to a
maximum height, then falls to the ground. The trajectory of the arrow
is noted. Which graph best represents the vertical velocity of the
arrow as a function of time? Ignore air resistance; the only force
acting is gravity.
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Answer
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The figure below shows five arrows with differing masses that were
launched straight up with the noted speeds. Rank the arrows, from
greatest to least, on the basis of the maximum height the arrows
reach. Ignore air resistance; the only force acting is gravity.
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Examples
Spud Webb, height 5'7", was one of the shortest basketball players
to play in the NBA. But he had an impressive vertical leap; he was
reputedly able to jump 110 cm off the ground. To jump this high,
with what speed would he leave the ground?
A football is punted straight up into the air; it hits the ground
5.2 s later. What was the greatest height reached by the ball?
With what speed did it leave the kicker’s foot?
Passengers on The Giant Drop, a free

fall ride at Six Flags Great
America, sit in cars that are raised to the top of a tower. The cars
are then released for 2.6 s of free fall. How fast are the passengers
moving at the end of this speeding up phase of the ride? If the cars
in which they ride then come to rest in a time of 1.0 s, what is
acceleration (magnitude and direction) of this slowing down phase
of the ride? Given these numbers, what is the minimum possible
height of the tower?
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Additional Clicker Questions
A particle moves with the position

versus

time graph shown. Which
graph best illustrates the velocity of the particle as a function of time?
Slide 2

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A.
B.
C.
D.
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A particle moves with the position

versus

time graph shown. Which
graph best illustrates the velocity of the particle as a function of time?
Slide 2

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A.
Answer
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A.
P and Q have the same velocity at 2 s.
B.
P and Q have the same velocity at 1 s and 3 s.
C.
P and Q have the same velocity at 1 s, 2 s, and 3 s.
D.
P and Q never have the same velocity.
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Masses P and Q move with the
position graphs shown. Do P and
Q ever have the same velocity? If
so, at what time or times?
Additional Clicker Questions
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A.
P and Q have the same velocity at 2 s.
Slide 2

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Masses P and Q move with the
position graphs shown. Do P and
Q ever have the same velocity? If
so, at what time or times?
Answer
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36
Additional Clicker Questions
Mike jumps out of a tree and lands on a trampoline. The
trampoline sags 2 feet before launching Mike back into the air. At
the very bottom, where the sag is the greatest, Mike’s
acceleration is:
A.
Upward
B.
Downward
C.
Zero
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Slide 2

37
Mike jumps out of a tree and lands on a trampoline. The
trampoline sags 2 feet before launching Mike back into the air. At
the very bottom, where the sag is the greatest, Mike’s
acceleration is:
A.
Upward
Answer
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Additional Examples
When you stop a car on icy pavement, the acceleration of your car
is approximately
–
1.0 m/s². If you are driving on icy pavement at 30
m/s (about 65 mph) and hit your brakes, how much distance will
your car travel before coming to rest?
As we will see in a future chapter, the time for a car to come to rest
in a collision is always about 0.1 s. Ideally, the front of the car will
crumple as this happens, with the passenger compartment staying
intact. If a car is moving at 15 m/s and hits a fixed obstacle, coming
to rest in 0.10 s, what is the acceleration? How much does the front
of the car crumple during the collision?
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