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Motion in
One Dimension
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v
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Honors Physics
Lecture Notes
ConcepTest 2.3
Position and Speed
1) yes
If the position of a car is
2) no
zero, does its speed have to
3) it depends on the
be zero?
position
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ConcepTest 2.3
Position and Speed
1) yes
If the position of a car is
2) no
zero, does its speed have to
3) it depends on the
be zero?
position
No, the speed does not depend on position, it depends on the change
of position. Since we know that the displacement does not depend on
the origin of the coordinate system, an object can easily start at x = –3
and be moving by the time it gets to x = 0.
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Wednesday August 31th
Introduction to 1-D Motion
Distance versus Displacement
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Average Speed
•Average speed describes how fast a particle is
moving. The equation is:
•where:
= average speed
= distance
= elapsed time
Average speed is
always a positive
number.
•The SI unit of speed is the (m/s).
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Average Velocity
•Average velocity describes how fast the
displacement is changing. The equation is:
•where:
= average velocity
= displacement
= elapsed time
Average velocity is
+ or – depending on
direction.
•The SI unit of speed is the (m/s).
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AVERAGE VELOCITY
The average velocity v x of a particle is defined as
vx 
x
x
x 2  x1

t
t 2  t1
x2
x
x1
t
t1
t2
t
Velocity is represented
by the slope on a
displacement-time graph
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Practice Problem: How long will it take the sound of a
starting gun to reach the ears of the sprinters if the starter
is stationed at the finish line for a 100 m race? Assume
that sound has a speed of about 340 m/s.
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Practice Problem: You drive in a straight line at 10 m/s for
1.0 km, then you drive in a straight line at 20 m/s for
another 1.0 km. What is your average velocity?
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Qualitative Demonstrations
1) Demonstrate the motion of a particle that has
an average speed and an average velocity that
are both zero.
Rock at Rest
2) Demonstrate the motion of a particle that has
an average speed and an average velocity that
are both nonzero.
Rock Distance and Displacement are the same
3) Demonstrate the motion of a particle that has
an average speed that is nonzero and an average
velocity that is zero.
Rock moves in a Complete Circle
4) Demonstrate the motion of a particle that has
an average speed that is zero and an average
velocity that is nonzero.
Does Not Happen
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Quantitative Demonstration
• You are a particle located at the origin.
Demonstrate how you can move from x = 0 m to
x = 5.0 m and back with an average speed of 0.5 m/s.
• What is the particle’s average velocity for the above
demonstration?
0.0 m/s, because displacement is 0.0 m.
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Graphical Problem
x
t
Demonstrate the motion of this particle.
Rock at Rest
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Graphical Problem
x
t
Demonstrate the motion of this particle.
Rock moving from rest with a positive constant velocity
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Graphical Problem
B
•
x
A
•
t
What physical feature of the graph gives the
constant velocity from A to B?
A Straight Line and slope
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Graphical Problem: Determine the average velocity from
the graph.
X (m)
3.0
2.0
1.0
0.0
t (s)
2.0
4.0
6.0
-1.0
-2.0
-3.0
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Graphical Review Problem
x
t
Demonstrate the motion of these two particles.
Blue Rock moving from rest at a higher constant velocity
Red Rock moving from rest at a lower constant velocity
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Graphical Problem
x
t
Demonstrate the motion of these two particles.
Blue Rock at rest, farthest from the origin (x = 0)
Red Rock at rest, closest to the origin (x = 0)
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Graphical Problem
x
t
What kind of motion does this graph represent?
Oscillatory motion, (almost) constantly changing
velocity
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Graphical Problem
x
0.82m
A
•
0.75s
• B0.22m
2.12s
t
Can you determine the average velocity from the
time at point A to the time at point B from this
graph?
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END
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