Position and displacement

1
Position anddisplacement
2
Objectives

• Describe motion in 1D using position, distance,
  and displacement.
• Analyze motion in 1D using position, distance,
  and displacement.
• Correctly use and interpret positive and negative
  values of position and displacement.

3
Assessment

• A robot car moves 200 m east, turns around and
  moves 600 m west. Describe this motion using
  position, displacement, and distance.
• A woman starts at x -10 m and has three
  successive displacements of -5 m. What is her
  final position?
• What displacement moves an object from a position
  of 25 meters to a position of -15 meters?

4
Physics terms

• origin
• position
• displacement

5
Equations
The final position equals the initial position
plus any displacements.
6
Describing motion
Before you can predict an objects motion, you
need to be able to describe it.
How do we describe an objects position? If the
object moves, what is the difference between its
distance and displacement?
7
Exploring the ideas
Click on this interactive on page 74.
8
Engaging with the concept
Initial position or final position can be entered
here.
9
Engaging with the concept
5
Enter a displacement of 5 meters
Click Enter
10
Engaging with the concept
5
5
5
Final position
Distance moved
11
Engaging with the concept
5
5
-10
5
Add a displacement of -10 meters
Click Enter
12
Engaging with the concept
Final position
15
5
-10
-5
Distance moved
13
Engaging with the concept
What is the difference between distance and
position?
15
5
-10
-5
14
Engaging with the concept
What is the difference between distance and
position?
Distance is always positive. It doesnt tell you
where you are because it has no direction
information.
15
5
-10
-5
15
Engaging with the concept
What is the difference between distance and
displacement?
15
5
-10
-5
16
Engaging with the concept
What is the difference between distance and
displacement?
Displacement is a change in position that
includes direction.
15
5
-10
-5
17
The position equation
The final position equals the initial position
plus any displacements.
How is position described?
18
Importance of the origin
In order to describe where something is, always
begin by deciding on an origin. All positions
can then be described by comparing them to the
origin.
19
Importance of the origin
GPS systems use 0 latitude and longitude as the
origin.
20
Position
Position tells you where you are relative to an
origin. Positive and negative values tell you
whether you are in front or behind, or to the
left or right of the origin.
21
The position equation
The final position equals the initial position
plus any displacements.
How is displacement described?
22
Coordinate systems
To describe displacement, you must create a
coordinate system and choose which direction is
positive and which is negative. This is a
choice! It may change for different problems.

Left - Right
-

Up Down
North South
West - East
-
23
Displacement
Displacement is a change in position. Positive
and negative values indicate direction.
24
Displacement is a vector
Displacement is a vector because it contains
direction information. For motion along a line,
direction is positive or negative.
25
Distance is a scalar
Distance is a scalar quantity. It does not
include direction information.
26
Adding displacements
An ant starts at 2 m, and crawls forward 7.1 m.
Then it turns around and crawls back 5.5 m. What
is the ants final position?
27
Adding displacements
An ant starts at 2 m, and crawls forward 7.1 m.
Then it turns around and crawls back 5.5 m. What
is the ants final position?
Add displacements graphically by drawing vectors
to scale

• The first vector starts at the initial position.
  
• The second vector starts at the end of the first
  vector.

28
Adding displacements
An ant starts at 2 m, and crawls forward 7.1 m.
Then it turns around and crawls back 5.5 m. What
is the ants final position?
You can also use numerical addition. This is
faster and more accurate.
29
Problem solving
How do you recognize the initial position and
displacements? What do you choose as the
initial position?
Example A boat sails 50 km north then 800 km
south. What is the sailboats final position?
30
Problem solving
How do you recognize the initial position and
displacements? What do you choose as the
initial position?
Example A boat sails 50 km north then 800 km
south. What is the sailboats final position?
Let the initial position be zero km When
nothing is said to establish a particular start
you may assume the initial position is zero.
31
Problem solving
How do you recognize the initial position and
displacements? What are the displacements?
Example A boat sails 50 km north then 800 km
south. What is the sailboats final position?
32
Problem solving
How do you recognize the initial position and
displacements? What are the displacements?
Example A boat sails 50 km north then 800 km
south. What is the sailboats final position?

• 50 km north is a displacement of 50 km
• 800 km south is a displacement of -800 km
• Displacements are movements, so words such as
  move, sail, run, and travel are clues.

33
Problem solving
How do you recognize the initial position and
displacements? What is the final position?
Example A boat sails 50 km north then 800 km
south. What is the sailboats final position?
34
Assessment

• A robot car moves 200 m east, turns around and
  moves 600 m west. Describe this motion using
  position, displacement, and distance.

35
Assessment

• A robot car moves 200 m east, turns around and
  moves 600 m west. Describe this motion using
  position, displacement, and distance.

The robot car starts at the origin with a
position of 0 m. It has a displacement of 200 m
east, and then a displacement of 600 m west.
Its final position is 400 meters west of the
origin. The total distance traveled is 800 m.
36
Assessment

1. A woman starts at x -10 m and has three
   successive displacements of -5 m. What is her
   final position?

37
Assessment

1. A woman starts at x -10 m and has three
   successive displacements of -5 m. What is her
   final position?

The final position is -25 m.
38
Assessment

1. What displacement moves an object from a position
   of 25 meters to a position of -15 meters?

Asked displacementGiven initial and final
positions
Relationships
Solution
Answer
39
Assessment

1. What displacement moves an object from a position
   of 25 meters to a position of -15 meters?

Asked displacementGiven initial and final
positions Relationships xf xi d
Solution d xf xi d -15 m 25 m
-40 m
Answer The displacement is -40 meters
40
Speed and velocity
41
Objectives

• Describe one dimensional motion using equations
  for speed and velocity.
• Analyze one dimensional motion using equations
  for speed and velocity.
• Define and identify positive and negative
  velocities.

42
Assessment

• A swallow moves 80 meters in 5.0 seconds. What
  is its speed? What is its velocity? How can the
  two be different?
• Write an English sentence that means the same as
  this equation
• Give an example of an object with positive
  position and negative velocity.

43
Physics terms

• speed
• velocity

44
Equations
The speed is the distance traveled divided by the
time taken. The velocity is the change in
position divided by the change in time.
45
Speed versus velocity
Are speed and velocity just two different words
for the same thing?

• In everyday life you probably use the words speed
  and velocity interchangeably.
• In physics class, speed and velocity are related,
  but not exactly the same.

46
Exploring the ideas
Click the interactive calculator on page 80 on
speed.
47
The speed equation
A car travels 30 meters in a trip that lasts 2.0
seconds. What is the cars speed?

30
2.0
Speed
48
The speed equation
A car travels 30 meters in a trip that lasts 2.0
seconds. What is the cars speed?
15 m/s
30
15
2.0
Speed
Click Run to see the car act out the meaning of
the equation.
49
The speed equation
If you go a distance of 45 meters at a speed of
16 m/s, how long does this trip last? What
variable are you solving for?
45
16
50
The speed equation
If you go a distance of 45 meters at a speed of
16 m/s, how long does this trip last?
2.8 seconds
45
16
2.81
Time
51
The speed equation
A fox runs at a speed of 9.7 m/s for 12
seconds. How far does the fox run?
9.7
12
52
The speed equation
A fox runs at a speed of 9.7 m/s for 12
seconds. How far does the fox run? 116
meters
116.4
9.7
12
Distance
53
How fast is fast?

• See if you can come up with an example of when an
  actual object might move at each speed.
• 0.1 m/s
• 1 m/s
• 10 m/s
• 100 m/s
• 1000 m/s

54
How fast is fast?

• See if you can come up with an example of when an
  actual object might move at each speed.
• 0.1 m/s about 0.22 mph (10 cm/s), the tip of
  the second hand on your clock
• 1 m/s
• 10 m/s
• 100 m/s
• 1000 m/s

55
How fast is fast?

• See if you can come up with an example of when an
  actual object might move at each speed.
• 0.1 m/s about 0.22 mph (10 cm/s), the tip of
  the second hand on your clock
• 1 m/s 2.2 mph, a slow walk
• 10 m/s
• 100 m/s
• 1000 m/s

This is an excellent benchmark to remember!
56
How fast is fast?

• See if you can come up with an example of when an
  actual object might move at each speed.
• 0.1 m/s about 0.22 mph (10 cm/s), the tip of
  the second hand on your clock
• 1 m/s 2.2 mph, a slow walk
• 10 m/s 22 mph, a brisk bike riding speed
• 100 m/s
• 1000 m/s

57
How fast is fast?

• See if you can come up with an example of when an
  actual object might move at each speed.
• 0.1 m/s about 0.22 mph (10 cm/s), the tip of
  the second hand on your clock
• 1 m/s 2.2 mph, a slow walk
• 10 m/s 22 mph, a brisk bike riding speed
• 100 m/s 220 mph, a supercars top driving speed
• 1000 m/s

58
How fast is fast?

• See if you can come up with an example of when an
  actual object might move at each speed.
• 0.1 m/s about 0.22 mph (10 cm/s), the tip of
  the second hand on your clock
• 1 m/s 2.2 mph, a slow walk
• 10 m/s 22 mph, a brisk bike riding speed
• 100 m/s 220 mph, a supercars top driving speed
• 1000 m/s 2,200 mph, about the F14 fighter
  jets top speed

59
Speed
speed

• Distance is always positive.
• Time is always positive.
• Therefore, speed is always positive!

So how do we tell the difference between moving
backward and forward?
60
Speed
speed

• Distance is always positive.
• Time is always positive.
• Therefore, speed is always positive!

So how do we tell the difference between moving
backward and forward?
We need a new variable velocity!
61
Velocity
velocity
The velocity is defined as the change in position
divided by the change in time.
62
Velocity
velocity
The velocity is defined as the change in position
divided by the change in time.
The symbol ? translates to the change in. If x
position then ?x means the change in position.
63
Velocity
velocity
The velocity is defined as the change in position
divided by the change in time.
What does ?t mean?
64
Velocity
velocity
The velocity is defined as the change in position
divided by the change in time.
What does ?t mean? If t time then ?t means
the change in time.
65
Velocity
velocity
The velocity is defined as the change in position
divided by the change in time.
A change in position, ?x, can be positive or
negative. That means that velocity can be
positive or negative.
66
Velocity
velocity
The velocity is defined as the change in position
divided by the change in time.
A change in position, ?x, can be positive or
negative. That means that velocity can be
positive or negative.
Moving forward is a positive velocity. Moving
backward is a negative velocity.
67
Velocity is a vector
Velocity can have negative or positive values.
The sign of the velocity tells you the direction
of motion. Velocity is a vector. A vector is a
type of variable which includes directional
information in a mathematically useful way.
68
Exploring the ideas
Click the interactive calculator on page 80 on
velocity.
69
The velocity equation
A car starts at 30 m and finishes at 10 m in a
trip that takes 2.0 seconds. Notice The change
in position is -20 m.
10
30
-20
2
What is the cars velocity?
2
0
Velocity
Enter your initial and final values here.
70
The velocity equation
A car starts at 30 m and finishes at 10 m in a
trip that takes 2.0 seconds. Notice The change
in position is -20 m.
10
30
-20
-10
2
What is the cars velocity? -10 m/s Click Run
and see the car drive backwards.
2
0
Velocity
71
The velocity equation
A car travels at 15 m/s. Four seconds after
starting out, it is at a position of 40 m. What
is the cars change in position? Where did the
car start from?
40
15
4
4
0
Change in position
72
The velocity equation
A car travels at 15 m/s. Four seconds after
starting out, it is at a position of 40 m. What
is the cars change in position? 60 m Where did
the car start from? -20 m
40
-20
60
15
4
4
0
Change in position
73
The change in position
What is the change in position?
The variable x stands for position. Subscript i
means initial and subscript f means final.
74
The change in position
What is the change in position?
?x xf xi (8 m) (2 m) 6 meters
75
Velocity
What is the velocity if the change in time (?t)
is 2 seconds?
76
Velocity
What is the velocity if the change in time (?t)
is 2 seconds?
The velocity is 3 m/s.
77
What if the person STARTS at 8 m and moves to the
left?
What is the velocity if the change in time (?t)
is 2 seconds?
78
What if the person STARTS at 8 m and moves to the
left?
What is the velocity if the change in time (?t)
is 2 seconds?
The man is heading in the negative direction so
he has a negative velocity.
79
Positive and negative positions and velocities
Can there be positive position and negative
velocity? I need a volunteer to show me how.
0

-
80
Positive and negative positions and velocities
Can there be positive position and negative
velocity?
Positive position
0

-
81
Positive and negative positions and velocities
Can there be positive position and negative
velocity?
Positive position
Negative velocity
0

-
82
Positive and negative positions and velocities
Can there be negative position and positive
velocity? I need a volunteer to show me how.
0

-
83
Positive and negative positions and velocities
Can there be negative position and positive
velocity?
Negative position
0

-
84
Positive and negative positions and velocities
Can there be negative position and positive
velocity?
Negative position
Positive velocity
0

-
85
Positive and negative positions and velocities
Can there be negative position and negative
velocity? I need a volunteer to show me how.
0

-
86
Positive and negative positions and velocities
Can there be negative position and negative
velocity?
Negative position
Negative velocity
0

-
87
Positive and negative positions and velocities
Can there be positive position and positive
velocity? I need a volunteer to show me how.
0

-
88
Positive and negative positions and velocities
Can there be positive position and positive
velocity?
Positive position
Positive velocity
0

-
89
The terminology of motion
Tell a story that illustrates how each picture
relates to the meaning of each word.
90
The terminology of motion
Tell a story that illustrates how each picture
relates to the meaning of each word.
For example A hiker needs to go southwest on a
map and this vector represents the hikers
movement.
91
Assessment

1. A swallow moves 80 meters in 5 seconds. What is
   its speed? What is its velocity? How can the two
   be different?

92
Assessment

1. A swallow moves 80 meters in 5 seconds. What is
   its speed? What is its velocity? How can the two
   be different?
2. Write an English sentence that means the same as
   this equation

The speed is 16 m/s. The velocity could be
either 16 m/s or -16 m/s depending on the
birds direction.
93
Assessment

1. A swallow moves 80 meters in 5 seconds. What is
   its speed? What is its velocity? How can the two
   be different?
2. Write an English sentence that means the same as
   this equation

The speed is 16 m/s. The velocity could be
either 16 m/s or -16 m/s depending on the
birds direction.
The velocity is the change in position divided by
the change in time.
94
Assessment

1. Give an example of an object with positive
   position and negative velocity.

95
Assessment

1. Give an example of an object with positive
   position and negative velocity.

A person to the right of the origin but walking
to the left would have a positive position and
negative velocity.
Negative velocity
Positive position
-

0