Transcript Operational definitions

Velocity

Operational definition:
d
v =
t
Three flavors of velocity
uniform
average
instantaneous
Uniform motion
d = 60 cm
d = 60 cm
t = 15 sec
t = 15 sec
Interpret: 60/15 = 4 cm/sec
d = 60 cm
d = 60 cm
t = 15 sec
t = 15 sec
Velocity

Operational definition:
d
v =
t
Three flavors of velocity
uniform
average
instantaneous
Graphing uniform motion
d = 60 cm
d = 60 cm
t = 15 sec
t = 15 sec
A graph is a collection of
points
Position
(cm)
120
60
0
0
5
10
15
20
Time (sec)
25
30
Uniform motion
A graph is a collection of
points
Position
(cm)
120
60
0
0
5
10
15
20
Time (sec)
25
30
Uniform motion
d = 60 cm
t = 15 sec
A graph is a collection of
points
Position
(cm)
120
60
0
0
5
10
15
20
Time (sec)
25
30
A graph is a collection of
points
Position
(cm)
120
60
0
0
5
10
15
20
Time (sec)
25
30
Uniform motion
d = 60 cm
d = 60 cm
t = 15 sec
t = 15 sec
A graph is a collection of
points
Position
(cm)
120
60
0
0
5
10
15
20
Time (sec)
25
30
A graph is a collection of
points
Position
(cm)
120
60
0
0
5
10
15
20
Time (sec)
25
30
A graph is a collection of
points
Position
(cm)
120
60
0
0
5
10
15
20
Time (sec)
25
30
How do we find the velocity?
rise
slope = run = d = velocity
t
Position
(cm)
120
= 4 cm/s
100
rise d = 60 cm
60
40
run t = 15 s
0
0
5
10
15
20
Time (sec)
25
30
Velocity

Operational definition:
d
v =
t
Three flavors of velocity
uniform
average
instantaneous
Average velocity

Left home at 5:00pm

At 6:00pm I was 60 miles from home

What was my velocity at 5:30pm?
Operational definition of
average velocity
d
vave =
t
Interpretation of average
velocity
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?
Start
Finish
Interpretation of average
velocity
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?
Start
Finish
Does this bullet have a velocity at
the instant shown?
picture courtesy of the late, great Doc Edgerton
Velocity

Operational definition:
d
v =
t
Three flavors of velocity
uniform
average
instantaneous
What is the velocity of this
truck?
t = 4 sec
t = 4 sec
What is the velocity at
t = 2 sec?
20
15
rise d
10
run t
5
5
4
3
2
1
0
0
Position (m)
Position (m)
25
Time (sec)
rise
slope = run = d = instantaneous velocity
t
Why use the tangent line?
20
15
10
5
Time (sec)
5
4
3
2
1
0
0
Position (m)
Position (m)
25
Let’s take a closer look
20
15
10
5
Time (sec)
5
4
3
2
1
0
0
Position (m)
Position (m)
25
Time (sec)
2.5
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
Position (m)
Position (m)
Let’s take a closer look
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
Time (sec)
2.5
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
Position (m)
Position (m)
Perhaps even closer
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
This is close enough
Position (m)
4.5
4.4
4.3
Position (m)
4.2
4.1
4
3.9
3.8
3.7
3.6
2.1
2.08
2.06
2.04
2.02
2
1.98
1.96
1.94
1.92
1.9
3.5
Time (sec)
The slope of this line is 4 m/s
What interpretation can we give to this slope?
Now extend this line in both directions
and it becomes the tangent
Position (m)
4.5
4.4
4.3
4.1
4
3.9
3.8
3.7
3.6
Time (sec)
2.1
2.08
2.06
2.04
2.02
2
1.98
1.96
1.94
1.92
3.5
1.9
Position (m)
4.2
Now extend this line in both directions
and it becomes the tangent
Position (m)
4.5
4.4
4.3
4.1
4
3.9
3.8
3.7
3.6
Time (sec)
2.1
2.08
2.06
2.04
2.02
2
1.98
1.96
1.94
1.92
3.5
1.9
Position (m)
4.2
25
20
15
10
5
Time (sec)
5
4
3
2
1
0
0
Position (m)
Position (m)
Instantaneous velocity
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?
How do you move a pencil to
create the following graph?
time
What is the corresponding
velocity versus time graph?
time
How do you move a pencil to
create the following graph?
time
What is the corresponding
velocity versus time graph?
time
How do you move a pencil to
create the following graph?
time
What is the corresponding
velocity versus time graph?
time
Slope = ?
time
Slope = ?
time
What’s the velocity at t=0?
30
Position (m)
25
20
15
10
5
0
0
1
2
3
Time (sec)
4
5
Graphing velocity
Velocity (m/s)
8
6
4
2
0
0
1
2
3
4
Time (sec)
5
6
What’s the velocity at t=1?
30
Position (m)
25
20
15
10
5
0
0
1
2
3
Time (sec)
4
5
Graphing velocity
Velocity (m/s)
8
6
4
2
0
0
1
2
3
4
Time (sec)
5
6
What’s the velocity at t=3?
30
Position (m)
25
20
15
10
5
0
0
1
2
3
Time (sec)
4
5
Graphing velocity
Velocity (m/s)
8
6
4
2
0
0
1
2
3
4
Time (sec)
5
6
What’s the velocity at t=4?
30
Position (m)
25
20
15
10
5
0
0
1
2
3
Time (sec)
4
5
Graphing velocity
Velocity (m/s)
8
6
4
2
0
0
1
2
3
4
Time (sec)
5
6
Graphing velocity
Velocity (m/s)
8
6
4
2
0
0
1
2
3
4
Time (sec)
5
6
How do you move a pencil to
create the following graph?
time
How do you move a pencil to
create the following graph?
+5
0
time
-5
Velocity
Read Chapter 2