motion and velocity displacement in time and space ft. per second mph meters/sec
Post on 25-Dec-2015
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Work = Force x Distance
Machines Produce Work by Transforming Energy or Changing the Direction or Distance Through Which a
Force Acts
Machines, Mechanisms and Motion are Intimately Related
Speed is the Rate of Displacement
10 ft.
Position A Position B
10
0
Seconds
sec/1sec10
10DistanceSpeed ft
ft
Time
Velocity is the Rate of Displacement in a Specified Direction
10 ft.Position A Position B
10
0
Seconds
sec/1sec10
10DistanceSpeed ft
ft
Time
EastSouth
WestNorth
Speed Equations
An object’s speed is a function of Displacement (change in position) and Time (change in time
between positions)
)(
)(
12
12
ttt
dddSpeed
Speed Equations
A simple and useful version of the Speed Equation Looks Like This
Time
DistanceSpeed
If You Want to Know the Distance Traveled
Time
DistanceSpeed
TimeSpeed Distance
You Can Rewrite the Equation Like This
Position-Time Graphs
Dis
tanc
e in
Fee
t
Time in Seconds0 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
6080
100120140160
180
20
2345678
9
1
40
Position-Time Graph
Dis
tanc
e in
Fee
t
Time in Seconds0 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.)
Run
RiseSlope
Time
DistanceSpeed
Rise
Run
Position-Time Graph
Dis
tanc
e in
Fee
t
Time in Seconds0 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.)
20sec.Δt
Speed = 20ft/sec.
Rise 80 ft.
Run 4 sec.
80ftΔd
Time
DistanceSpeed
4sec.
80ftSpeed
Position-Time Graph
Dis
tanc
e in
Fee
t
Time in Seconds0 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 remains constant
Position-Time Graph
Dis
tanc
e in
Fee
t
Time in Seconds0 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
Average Speed Time GraphsSp
eed
in f
t/se
cond
Time in Seconds0 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 that follow
Spee
d in
ft/
seco
nd
Time in Seconds0 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
Spee
d in
ft/
seco
nd
Time in Seconds0 1 2 3 4 5 6 7 8 9
10
30
40
50
20
Answer: 40 ft/second
Average Speed Time Graphs
Spee
d in
ft/
seco
nd
Time in Seconds0 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
Spee
d in
ft/
seco
nd
Time in Seconds0 1 2 3 4 5 6 7 8 9
10
30
40
50
20
Answer: This Thing Traveled a total of 175 FeetDistance = 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
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 Quantity
Speed is a Scalar Quantity
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!
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
Point B Point C
Point A
Vectors Can Describe Displacement
Total Displacement12.2 miles North East of the
Starting Position
10 miles East
7 miles North
The Black Dashed Line is called th
e Resultant
The magnitude of the Resultant Vector is found using the Pythagorean Theorem.
B2
C2
A2
A2 + B2 = C2
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