I: Intro to Kinematics: Motion in
One Dimension
AP Physics C
Mrs. Coyle
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Particle Model
Position Vector
Displacement, distance
Average Velocity, Average Speed
Instantaneous Velocity, Instantaneous Speed
Intro to the Derivative.
Graphical Analysis (position vs time)
Uniform Linear Motion
Video Clip of Oil Spill in Gulf
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http://www.youtube.com/watch?v=_2EXDmn
NPw0
Motion
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Motion is relative
Origin
Position is compared to an origin
Coordinate system or a reference frame
Motion Diagram
t=0.75 sec
t=0.50 sec
t=0.25 sec
t=0 sec
Particle Model
t=0
. .
.
t=0.25s
.
t=0.50s
t=0.75s
.
Position Vectors
y=+4 m
o
x= -5m
x= 5m
Position (m)
x= 10 m
Position Vectors
o
x=10m
Position (m)
x=20m
Vectors and Scalars
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Scalars  Magnitude (size)
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Vectors  Magnitude and Direction
Displacement (Dx): change in position.
Dx =xf - xi
Dx
o
x1=15m
Position, x (m)
x2=20m
Distance and Displacement
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Distance:
(Scalar)
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Displacement Dx =xf - xi
(Vector)
Average Speed and Average Velocity
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Average Speed= Total Distance Travelled
Time
(Scalar)
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Average Velocity=
Displacement =
Time
Dx
Dt
(Vector)
Prob. #2.4
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A particle moves according to the equation
x=10t2 (x in meters, t in seconds).
Find the average velocity for the time
interval from 2s to 3s.
Ans: 50m/s
Instantaneous Speed
Instantaneous Velocity
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Instantaneous Speed
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Instantaneous Velocity
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Speed at a given instant. (Time is very very small)
Velocity at a given instant. (Time is very very small)
Instantaneous speed is the magnitude of
instantaneous velocity.
Instantaneous Velocity:
the limit of Dx as Dt approaches 0.
Dt
lim Dx
Dt 0
Dt
v=
v=
dx
dt
Instantaneous Velocity (or simply)
Velocity is the derivative of x with
respect to t.
v=
dx
dt
Instantaneous Velocity
 Instantaneous
speed is the
magnitude of instantaneous
velocity.
Graphical Analysis of Motion
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Position vs Time
Velocity vs Time
Acceleration vs Time
Example 1: Graph of Position vs Time
Position
(m/s)
o
Time (s)
•Slope of Line= Average Velocity
•In this case does the slope also
equal the instantaneous velocity?
Uniform Linear Motion
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Motion with constant velocity
 Straight line
 Same direction
Example 2: Graph of Position vs Time
Position
(m)
o
Time (s)
Instantaneous Velocity at a given time=
Slope of Tangent at that time
Example 2: Graph of Position vs Time
Position
40.0
(m)
20.0
o
Time (s)
2.0
Find the instantaneous velocity at 2sec
and the average velocity from 0 to 2sec.
Example 3: Position vs Time Graph
Position, (m)
20.0
10.0
A
o
0.5
-10.0
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1.0
1.5
2.0
Time, (s)
At what time(s) was the object at the origin?
What is the average velocity from 0 to 1sec, 1 to
1.5 sec and 0 to 2sec?