How Do We Describe Motion?

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How Do We Describe Motion?

• Motion in 1-D

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Adding vectors To add vectors graphically they
must be placed tip to tail. The result (F1
F2) points from the tail of the first vector to
the tip of the second vector.
F1
F2
For collinear vectors
Fnet ?
F1
F2
Fnet ?
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Adding Vectors
Length b
Length a
c
T b a
a2 b2 c2
Tan ? b/a
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Adding Vectors

• Can also add

• Same result as before

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Components
ac cos? bc sin?
c
b
?
a2 b2 c2
a
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How fast is this plane moving?
200
100
Cross wind
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Velocity
Velocity is a vector that measures how fast and
in what direction something moves.
? is a symbol it is not a quantity
?r is the (vector) displacement Speed is the
magnitude of the velocity. It is a scalar.
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More general motion, non uniform motion
On a graph of position versus time, the average
velocity is represented by the slope of a chord.
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This is represented by the slope of a line
tangent to the curve on the graph of an objects
position versus time.
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Slide 2-16
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Motion diagram (student walking to school)
Graph
Table of data
Slide 2-13
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Checking Understanding
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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Answer
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.
A.
B.
D.
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Checking Understanding
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?
A.
B.
C.
D.
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Answer
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?
A.
B.
C.
D.
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Velocity

• The velocity is a vector. It changes if we change
• the speed
• the direction i.e. driving around a curve even at
  constant speed.

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Finding d when we know v Consider only x
component ?x vx ?t or xf xi vx ?t If vx
v1 (constant) vx ?t is the same as the area in
graph of v /t
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If V is not constant we can still use area in
graph
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Example Speedometer readings are obtained and
graphed as a car comes to a stop along a
straight-line path. How far does the car move
between t 0 and t 16 seconds?
Since there is not a reversal of direction, the
area between the curve and the time axis will
represent the distance traveled.
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Example Problem
A soccer player is 15 m from her opponents 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 kickers
foot?
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acceleration

• Acceleration is a vector
• (since v is a vector)

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• Which has a greater acceleration an airplane
  going from 1000 km/hr to 1005 km/hr in 5 seconds
  or a skateboarder going from 0 to 5 km/hr in 1
  second?
• The airplane
• The skateboarder

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Acceleration

• Acceleration is
• The rate of change of velocity
• The slope of a velocity-versus-time graph

Slide 2-26