Gears Motion and Velocity

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Motionand

VelocityDisplacement in Time and Space

Ft. Per Second

MPH

Meters/Sec.

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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

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Motion or Movement is a Change In

Position Called Displacement

10 ft.

Position A

Position B

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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 

−∆

−∆

=

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Speed Equations

A simple and useful version of the

Speed Equation Looks Like This

Time

Distance=

Speed 

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If You Want to Know the

Distance Traveled

Time

Distance=Speed 

TimeSpeed ⋅=Distance

You Can Rewrite the Equation Like

This

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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

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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

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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

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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 ∆=∆

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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

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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

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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

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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

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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!