gears motion and velocity
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8/3/2019 Gears Motion and Velocity
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Motionand
VelocityDisplacement in Time and Space
Ft. Per Second
MPH
Meters/Sec.
8/3/2019 Gears Motion and Velocity
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Work = Force x Distance
Machines Produce Work by
Transforming Energy or Changing theDirection or Distance Through Which a
Force Acts
Machines, Mechanisms and
Motion are Intimately Related
8/3/2019 Gears Motion and Velocity
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Motion or Movement is a Change In
Position Called Displacement
10 ft.
Position A
Position B
8/3/2019 Gears Motion and Velocity
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Speed is the Rate of Displacement
10 ft.
Position APosition B
10
0
Seconds
sec/1sec11
11DistanceSpeed ft ft Time
===
8/3/2019 Gears Motion and Velocity
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Velocity is the Rate of Displacement
in a Specified Direction
10 ft.
Position APosition B
10
0
Seconds
sec/1sec11
11DistanceSpeed ft
ft
Time===
E a s t S o u t h
W e s t
N o r t h
8/3/2019 Gears Motion and Velocity
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Speed Equations
An object’s speed is a function of Displacement
(change in position) and Time (change in time
between positions)
)()(
11
11
t t t d d d Speed
−∆
−∆
=
8/3/2019 Gears Motion and Velocity
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Speed Equations
A simple and useful version of the
Speed Equation Looks Like This
Time
Distance=
Speed
8/3/2019 Gears Motion and Velocity
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If You Want to Know the
Distance Traveled
Time
Distance=Speed
TimeSpeed ⋅=Distance
You Can Rewrite the Equation Like
This
8/3/2019 Gears Motion and Velocity
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Position-Time Graphs
D i s t a n c e i
n F e e t
Time in Seconds
0 1 2 3 4 5 6 7 8 9
40
120
160
200
80
Describes the Rate of Change in
Position of an Object Over Time
Distance (ft) Vs. Time (sec.)DistanceTime
60
80100
120
140
160
180
20
2
3
45
6
7
8
9
1
40
8/3/2019 Gears Motion and Velocity
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Position-Time Graph
D i s t a n c e i
n F e e t
Time in Seconds
0 1 2 3 4 5 6 7 8 9
40
120
160
200
80
The Slope is Equivalent to the
Average Speed
Distance (ft) Vs. Time (sec.)RunRiseSlope =
TimeDistanceSpeed =
Rise
Run
8/3/2019 Gears Motion and Velocity
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Position-Time Graph
D i s t a n c e i
n F e e t
Time in Seconds
0 1 2 3 4 5 6 7 8 9
40
120
160
200
80
How Fast is this Object Moving?
Distance (ft) Vs. Time (sec.)
sec.11Δt =
Speed = 20ft/sec.
Rise80 ft.
Run 4
sec.
ft11Δd =
Time
DistanceSpeed
∆
∆=
sec.1
ft11Speed =
8/3/2019 Gears Motion and Velocity
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Position-Time Graph
D i s t a n c e i
n F e e t
Time in Seconds
0 1 2 3 4 5 6 7 8 9
40
120
160
200
80
Distance (ft) Vs. Time (sec.)
The Slope of this Line Remains
Constant Throughout the Graph
The
constant
slope
indicates
that the
speed of the
object
remainsconstant
8/3/2019 Gears Motion and Velocity
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Position-Time Graph
D i s t a n c e i
n F e e t
Time in Seconds
0 1 2 3 4 5 6 7 8 9
40
120
160
200
80
The Speed of
This Object
Changes
Over Time
Distance (ft) Vs. Time (sec.)
B
C
A
Speed @C = 50 ft/secSpeed @A = 5 ft/sec Speed @B = 24 ft/sec
The Object is
Accelerating
VelocitySlope ∆=∆
8/3/2019 Gears Motion and Velocity
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Average Speed Time Graphs
S p e e d
i n f t / s e c o n d
Time in Seconds
0 1 2 3 4 5 6 7 8 9
10
30
40
50
20
Describes the speed of an object at specific times
and the total displacement but NOT the Direction
Study this graph and answer the questions thatfollow
8/3/2019 Gears Motion and Velocity
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S p e e d
i n f t / s e c o n d
Time in Seconds
0 1 2 3 4 5 6 7 8 9
10
30
40
50
20
How fast was this thing moving, 5 Seconds after it
began to move?
Hint: It began moving after 1 second
Average Speed Time Graphs
8/3/2019 Gears Motion and Velocity
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S p e e d
i n f t / s e c o n d
Time in Seconds
0 1 2 3 4 5 6 7 8 9
10
30
40
50
20
Answer: 40 ft/second
Average Speed Time Graphs
8/3/2019 Gears Motion and Velocity
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S p e e d
i n f t / s e c o n d
Time in Seconds
0 1 2 3 4 5 6 7 8 9
10
30
40
50
20
What was the total Displacement of this thing?How far did the thing go during the whole trip?
Average Speed Time Graphs
8/3/2019 Gears Motion and Velocity
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S p e e d
i n f t / s e c o n d
Time in Seconds
0 1 2 3 4 5 6 7 8 9
10
30
40
50
20
Answer: This Thing Traveled a total of 175 Feet
Distance = Speed x Time. Therefore the total
distance is the sum of the areas of each of the
5 rectangles! Try it….It works.
Average Speed Time Graphs
8/3/2019 Gears Motion and Velocity
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Another Difference Between
Speed and Velocity
Scalar Quantities
(One Number)
One Gallon
Distance
Speed (MPH)
Voltage
Vector Quantities
(More Than One Number)
Machine Screw Specification
(tpi,length,diameter,head style)
Pant Sizes (Waist and Length)
Velocity (Speed and Direction)
Velocity is a Vector
QuantitySpeed is a Scalar
Quantity
8/3/2019 Gears Motion and Velocity
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Vectors Graphically Describe
DIRECTION and MAGNITUDE
One
Foot/sec
One
Foot/sec
One
Foot/sec++
=
3 Feet/sec
And You can Add and subtract
Them!
8/3/2019 Gears Motion and Velocity
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The Length of a Vector is Proportional to It’s
Magnitude
6 Centimeters
6 MPH
A Vector Describing a Velocity of 6 MPH is
Drawn With a Length of 6 Units
6 Inches
Scaling Vectors
8/3/2019 Gears Motion and Velocity
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Point B Point C
Point A
Vectors Can Describe Displacement
Total Displacement
12.2 miles North East of theStarting Position
10 miles East
7 miles
North
T h e B
l a c k D a s h
e d L i n e
i s c a l l e
d t h e R e s u
l t a n t
The magnitude of the Resultant
Vector is found using the
Pythagorean Theorem.
B2
C2
A2
A2 + B2 = C2
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The End
Now…….Get Moving!
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