velocity operational definition: dd tt v= three flavors of velocity uniform average instantaneous
TRANSCRIPT
![Page 1: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/1.jpg)
Velocity Operational definition:
dt
v =
Three flavors of velocityuniformaverageinstantaneous
![Page 2: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/2.jpg)
Uniform motion
d = 60 cm
t = 15 sec
d = 60 cm
t = 15 sec
![Page 3: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/3.jpg)
Interpret: 60/15 = 4 cm/sec
d = 60 cm d = 60 cm
t = 15 sec t = 15 sec
![Page 4: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/4.jpg)
Velocity Operational definition:
dt
v =
Three flavors of velocityuniformaverageinstantaneous
![Page 5: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/5.jpg)
Graphing uniform motion
d = 60 cm d = 60 cm
t = 15 sec t = 15 sec
![Page 6: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/6.jpg)
A graph is a collection of points
Time (sec)
Position (cm)
5 10 15 20 25 30
60
120
00
![Page 7: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/7.jpg)
Uniform motion
![Page 8: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/8.jpg)
A graph is a collection of points
Time (sec)5 10 15 20 25 30
60
120
00
Position (cm)
![Page 9: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/9.jpg)
Uniform motion
d = 60 cm
t = 15 sec
![Page 10: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/10.jpg)
A graph is a collection of points
Time (sec)5 10 15 20 25 30
60
120
00
Position (cm)
![Page 11: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/11.jpg)
A graph is a collection of points
Time (sec)5 10 15 20 25 30
60
120
00
Position (cm)
![Page 12: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/12.jpg)
Uniform motion
d = 60 cm d = 60 cm
t = 15 sec t = 15 sec
![Page 13: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/13.jpg)
A graph is a collection of points
Time (sec)5 10 15 20 25 30
60
120
00
Position (cm)
![Page 14: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/14.jpg)
A graph is a collection of points
Time (sec)5 10 15 20 25 30
60
120
00
Position (cm)
![Page 15: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/15.jpg)
A graph is a collection of points
Time (sec)5 10 15 20 25 30
60
120
00
Position (cm)
![Page 16: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/16.jpg)
How do we find the velocity?
Time (sec)5 10 15 20 25 30
60
120
00
rise d
run t
slope = riserun = d
tvelocity =
= 4 cm/s
Position (cm)
40
100
= 60 cm
= 15 s
![Page 17: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/17.jpg)
Velocity Operational definition:
dt
v =
Three flavors of velocityuniformaverageinstantaneous
![Page 18: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/18.jpg)
Average velocity Left home at 5:00pm
At 6:00pm I was 60 miles from home
What was my velocity at 5:30pm?
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Operational definition of average velocity
dt
vave =
![Page 20: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/20.jpg)
Interpretation of average velocity
Start Finish
The hare’s average velocity is the uniform velocity of the tortoise. In other words, how fast would the tortoise have to plod along to start and finish the race at the same time as the hare?
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Interpretation of average velocity
Start Finish
Problem: If the hare traveled at a uniform 10 miles/hour for the first hour and a uniform 4 miles/hour for the last two hours, what was the hare’s average velocity?
What was the tortoise’s uniform velocity?
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Does this bullet have a velocity at the instant shown?
picture courtesy of the late, great Doc Edgerton
![Page 23: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/23.jpg)
Velocity Operational definition:
dt
v =
Three flavors of velocityuniformaverageinstantaneous
![Page 24: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/24.jpg)
What is the velocity of this truck?
t = 4 sec t = 4 sec
![Page 25: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/25.jpg)
Time (sec)
Posit
ion
(m
)
0
5
10
15
20
25
0 1 2 3 4 5
What is the velocity at t = 2 sec?
rise d
run t
slope = riserun = d
tinstantaneous velocity =
Pos
itio
n (m
)
![Page 26: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/26.jpg)
Time (sec)
Posit
ion
(m
)
0
5
10
15
20
25
0 1 2 3 4 5
Why use the tangent line?
Pos
itio
n (m
)
![Page 27: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/27.jpg)
Let’s take a closer look
Time (sec)
Posit
ion
(m
)
0
5
10
15
20
25
0 1 2 3 4 5
Pos
itio
n (m
)
![Page 28: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/28.jpg)
Let’s take a closer look
Time (sec)
Posit
ion
(m
)
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
1.5
1.6
1.7
1.8
1.9 2
2.1
2.2
2.3
2.4
2.5
Pos
itio
n (m
)
![Page 29: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/29.jpg)
Perhaps even closer
Time (sec)
Posit
ion
(m
)
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
1.5
1.6
1.7
1.8
1.9 2
2.1
2.2
2.3
2.4
2.5
Pos
itio
n (m
)
![Page 30: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/30.jpg)
This is close enough
Time (sec)
Po
sit
ion
(m
)
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
1.9
1.9
2
1.9
4
1.9
6
1.9
8 2
2.0
2
2.0
4
2.0
6
2.0
8
2.1
The slope of this line is 4 m/s
What interpretation can we give to this slope?
Pos
itio
n (m
)
![Page 31: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/31.jpg)
Time (sec)
Po
sit
ion
(m
)
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
1.9
1.9
2
1.9
4
1.9
6
1.9
8 2
2.0
2
2.0
4
2.0
6
2.0
8
2.1
Now extend this line in both directions and it becomes the tangent
Pos
itio
n (m
)
![Page 32: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/32.jpg)
Now extend this line in both directions and it becomes the tangent
Time (sec)
Po
sit
ion
(m
)
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
1.9
1.9
2
1.9
4
1.9
6
1.9
8 2
2.0
2
2.0
4
2.0
6
2.0
8
2.1
Pos
itio
n (m
)
![Page 33: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/33.jpg)
Time (sec)
Posit
ion
(m
)
0
5
10
15
20
25
0 1 2 3 4 5
Instantaneous velocity
Pos
itio
n (m
)
![Page 34: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/34.jpg)
Consider the following statement: “d/t gives the velocity for an
interval. If we want the velocity at just one instant, we would divide the position at that instant by the time at that instant: v = d/t.” Is this right?
It’s 12 noon and I’m in Silver Bay.....how fast am I going?
![Page 35: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/35.jpg)
How do you move a pencil to create the following graph?
time
pos
itio
n
![Page 36: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/36.jpg)
What is the corresponding velocity versus time graph?
time
velo
city
![Page 37: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/37.jpg)
How do you move a pencil to create the following graph?
time
pos
itio
n
![Page 38: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/38.jpg)
What is the corresponding velocity versus time graph?
time
velo
city
![Page 39: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/39.jpg)
How do you move a pencil to create the following graph?
time
pos
itio
n
![Page 40: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/40.jpg)
What is the corresponding velocity versus time graph?
time
velo
city
![Page 41: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/41.jpg)
Slope = ?
time
pos
itio
n
![Page 42: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/42.jpg)
Slope = ?
time
pos
itio
n
![Page 43: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/43.jpg)
0
5
10
15
20
25
30
0 1 2 3 4 5
Time (sec)
Posi
tion (m
)
What’s the velocity at t=0?
![Page 44: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/44.jpg)
Graphing velocity
Time (sec)
Vel
ocit
y (m
/s)
1 2 3 4 5 6
2
4
00
6
8
![Page 45: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/45.jpg)
0
5
10
15
20
25
30
0 1 2 3 4 5
Time (sec)
Posi
tion (m
)
What’s the velocity at t=1?
![Page 46: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/46.jpg)
Graphing velocity
Time (sec)1 2 3 4 5 6
2
4
00
6
8
Vel
ocit
y (m
/s)
![Page 47: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/47.jpg)
0
5
10
15
20
25
30
0 1 2 3 4 5
Time (sec)
Posi
tion (m
)
What’s the velocity at t=3?
![Page 48: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/48.jpg)
Graphing velocity
Time (sec)1 2 3 4 5 6
2
4
00
6
8
Vel
ocit
y (m
/s)
![Page 49: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/49.jpg)
0
5
10
15
20
25
30
0 1 2 3 4 5
Time (sec)
Posi
tion (m
)
What’s the velocity at t=4?
![Page 50: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/50.jpg)
Graphing velocity
Time (sec)1 2 3 4 5 6
2
4
00
6
8
Vel
ocit
y (m
/s)
![Page 51: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/51.jpg)
Graphing velocity
Time (sec)1 2 3 4 5 6
2
4
00
6
8
Vel
ocit
y (m
/s)
![Page 52: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/52.jpg)
How do you move a pencil to create the following graph?
time
velo
city
![Page 53: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/53.jpg)
How do you move a pencil to create the following graph?
time
velo
city
+5
-5
0
![Page 54: Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f155503460f94c2a300/html5/thumbnails/54.jpg)
Velocity
Read Chapter 2