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Chapter 2: Linear Motion
Mr. Miller
Conceptual
Physics
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• Motion is relative
• An object’s motion is always
described in reference to another
object
Relative Motion
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• When an object is said to be
traveling at 60 km/h, it is implied
that it is moving at 60 km/h
relative to the Earth.
Relative Motion
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Jamiroquai
“Virtual Insanity”
Travelling Without Moving
1997 Video of the Year
Relative Motion
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Relative Motion: Virtual Insanity
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Vector- a quantity possessing both
magnitude and direction
Scalar- a quantity possessing only
magnitude
Vectors and Scalars
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Examples of Vectors:
• Displacement (Δx)
• Velocity (v)
• Acceleration (a)
• Force (F)
• Momentum (p)
Vectors and Scalars
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Examples of Scalars:
• Distance (d)
• Mass (m)
• Speed (v)
• Time (t)
Vectors and Scalars
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Instantaneous speed: the speed
that something has at any one
instance
Average speed: the speed of an
object over a time interval
Speed
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Speed
The average speed for a trip might
be 53 miles/hour.
...or 70 miles/hour on the open road.
However, during this trip your
instantaneous speed might have
been 0 miles/hour at a stoplight...
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Speed
What are the units of speed?
• miles/hour…………….mph
• kilometer/hour……….km/h
• meters/second……….m/s
• furlongs/fortnight?
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Speed
1. What is the average speed of a cheetah
that sprints 100 meters in 4 seconds?
2. How about if it sprints 50 m in 2 s?
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Velocity
Velocity = {speed with a direction}
Examples:
70 mph is a speed.
70 mph North is a velocity.
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Velocity
What are the units of velocity?
Velocity has the same units as
speed except they also have a
direction
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Velocity and speed equations
atvv 12
0112 tvxx
)(2 12
2
1
2
2 xxavv
012 vv2
21
112 attvxx
02
1
2
2 vv
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Velocity vs. speed
The speedometer of a car moving to the
east reads 100km/h. It passes another
car that moves to the west at 100km/h.
• Do both cars have the same speed?
• Do they have the same velocity?
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• In an unusual move by the New York State
Department of Transportation, all of the "speed
limit" signs were replaced with "velocity limit"
signs.
– What would such a sign look like?
– How could one travel faster than the old speed limit
without violating the new velocity limit?
Conceptual Review
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• Which device(s) on a car can
be used to change …
–its speed?
–its velocity but not its speed?
Conceptual Review
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• A car driving on a circular test track shows a
constant speedometer reading of 100 kph for
one lap.
– Describe the car's speed during this time.
– Describe its velocity.
– How do the speed and velocity compare?
Conceptual Review
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• Is it possible for an object to have …
–constant speed and changing
velocity,
–changing speed and constant
velocity?
Conceptual Review
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• Why are the devices in cars
called speedometers and
not velocitometers?
Conceptual Review
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OK Go
“Here It Goes Again”
Oh No
2007 Grammy award for "Best Short-Form Music Video”
Relative Motion…one more time
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Relative Motion…one more time
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Acceleration
Acceleration is the rate of change of velocity.
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Acceleration
What are the units of acceleration?
• miles/hour/second…………….mi/h/s
• kilometer/hour/second……….km/h/s
• meters/second/second……….m/s/s or m/s2
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Acceleration equations
atvv 12
2
21
112 attvxx
)(2 12
2
1
2
2 xxavv
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Acceleration
Acceleration is the positive or
negative depending on the
direction of the acceleration.
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Acceleration
An object traveling with a constant positive velocity
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Acceleration
An object traveling with a constant negative velocity
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Acceleration
An object traveling with a positive velocity, positive acceleration.
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Acceleration
An object traveling with a positive velocity, negative acceleration.
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Acceleration
An object traveling with a negative velocity, negative acceleration.
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Acceleration
An object traveling with a negative velocity, positive acceleration.
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Free fall
Free fall is a state of falling free
from air resistance and other forces
except gravity.
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Free fall
All free-falling objects
(on Earth) accelerate
downwards at a rate of
approximately 10 m/s2
(to be exact, 9.8 m/s2).
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Free fall
Acceleration due to gravity = g
g = -9.8 m/s2
In some worksheets we will estimate g = -10 m/s2
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In the absence of air
resistance, all objects
fall with the same
acceleration,
although this may be
hard to tell by testing
in an environment
where there is air
resistance.
Free fall
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Coin and Feather Movie
Free fall
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Feather and Hammer on the Moon Movie
Free fall
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For objects dropped from rest
(v1 = 0 m/s)
atvv 12
2
21
12 0 atxx
)(2 12
2
1
2
2 xxavv
atv 02
2
21
112 attvxx
)(20 12
2
2 xxav
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Time for a Gizmo!
Free fall
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A ball is thrown up with an
initial velocity of 19.6 m/s.
What will the velocity and
displacement of the ball be after
1 second? 2 seconds? 3 seconds?
4 seconds ? Use -9.8 m/s2 for g.
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Graphs of Motion
On a displacement vs. time graph the slope of
the line is equal to the velocity of the object.
On a velocity vs. time graph the slope of the line
is equal to the acceleration of the object.
On a velocity vs. time graph the area underneath
the curve is equal to the displacement of the object.
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Graphs of Motion
An object traveling with a constant positive velocity
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Graphs of Motion
An object traveling with a constant negative velocity
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Graphs of Motion
An object traveling with a positive velocity, positive acceleration.
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Graphs of Motion
An object traveling with a positive velocity, negative acceleration.
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Graphs of Motion
An object traveling with a negative velocity, negative acceleration.
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Graphs of Motion
An object traveling with a negative velocity, positive acceleration.
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x vs. t graph v vs. t graph
Describe the motion.Object standing still at 20 m.
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x vs. t graph v vs. t graph
Describe the motion.Object traveling at a constant 10 m/s
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x vs. t graph v vs. t graph
Describe the motion.Object traveling at a constant -10 m/s
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x vs. t graph v vs. t graph
Describe the motion.Object traveling at a constant 20 m/s for
2 seconds and then stands still at 40 m.
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x vs. t graph v vs. t graph
Describe the motion.Object traveling at a constant 20 m/s for
2 sec and then a constant -20 m/s for 2 sec.
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x vs. t graph v vs. t graph
Describe the motion.Object traveling at a constant negative velocity, stops for
a while, then travels at a positive velocity.
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x vs. t graph v vs. t graph
Describe the motion.Object traveling at a constant
acceleration of 0.2 m/s2.
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x vs. t graph v vs. t graph
Describe the motion.Object traveling at a constant
acceleration of -0.2 m/s2.
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x vs. t graph v vs. t graph
Describe the motion.Object traveling at a constant acceleration of -0.2 m/s2.
Notice the velocity goes from being positive to negative.