### What are the Essentials to describing motion?

```WHAT ARE THE ESSENTIALS TO
DESCRIBING MOTION?
How do you know whether
something is moving or not?
the teacher is holding.
 What happens to the telescope as you follow the
object?
 Now carefully observe your teacher’s telescope.
 Was the ball “moving” during the two
experiments? Explain.
How can we describe motion?
 What is a Reference frame? A reference frame
includes three essential components:
 1. An object of reference, which is a real object in the
physical world.
 2. A clearly defined coordinate system.
 The coordinate system includes labels for the direction of
the axis, such as north, south, east, west, left, right, up
down, or positive and negative.
 The unit scale for measuring distances is also identified.
 A point on the coordinate system, usually the 0 point, is
attached to the object of reference.
 3. A clock which includes an origin t = 0 and a unit of
measurement for specifying times and time
intervals.
Consider the following…
 • A blue car moves along a street with two
passengers. One sits in the front passenger
seat of the car and the other passenger sits in
the back seat.
• A red car moves in the same direction and is
passing the blue car.
• A green car moving faster than the blue car, is
directly behind the blue car
• There is a sidewalk along the road the cars are
traveling and a pedestrian is standing on the
sidewalk.
Examine the map below. Your friend is visiting Washington
DC and is staying at George Washington University. Your
friend must walk across town to get to the Smithsonian
Institution
What are assumptions?
 Assumptions are issues we take for granted in an
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experiment.
They can help us explain why the results weren’t
exactly as we expected or could be something that
wasn’t taken into account when we designed the
experiment.
Despite the outcome of the experiment, it’s
important to consider the assumptions that may
Assumptions are factors that could affect our results,
but have not been included in our calculations or
reasoning.
What are some assumptions that may affect the
time you tell your friend to leave?
How can we define “motion”?
 Use what you have learned to define
“motion”.
 Motion: An object is in motion with respect to
another object (reference object) if, as time
progresses, its position is changing relative to
the reference
object.
Am I in motion?
What is the scientific
method?
 State the problem (question): How is the
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motion of the ball and the marks related?
Form a hypothesis: If…then…
Analyze your data: Observe, make tables and
graphs
Draw Conclusions: Are there any
relationships?
What is a motion dot
diagram?
 One representation of motion is called a dot
diagram. To make a dot diagram mark
locations of a moving object at equal time
intervals.
 Describe
the motion
of objects
A,B,C.
Space and position
 In physics, the word position refers to the location
of an object at one instant.
 A position is always specified relative to an origin.
 The net change in position relative to the origin is
called displacement (takes into consideration
direction).
Position and distance
 Distance is related to, but different from, position.
 Distance is a measure of length of path taken
without regard to direction.
 What distance did the man below travel?
 What is the final position (displacement) from the
origin?
What is a vector quantity?
 Scalar Quantity: Has magnitude (# or
quantity) such as time, distance, speed
 Vector Quantity: Has magnitude and
direction such as displacement and velocity.
What is an index?
 An index is a number that helps people
compare things.
 • Miles per gallon is an index of how well a car
uses gas.
 • Batting average is an index of how well a
baseball player hits.
 • Grades are an index of how well students
perform on a test.
How do we determine the
“steepness” index?
Rules for the Index
1. Each slide gets one steepness index because
it has the same steepness all the way down.
2. You have to use the exact same procedure for
each slide to find its index.
3. A big index value should mean that the slide
is steep. A small index number should mean
that the slide is less steep
How do we make a graph of
Popping Index
18
Number Popped Kernels
16
14
12
10
8
6
4
2
0
0
2
4
6
8
Time (sec)
10
12
14
What is velocity?
 Velocity of an object moving at constant velocity
is the slope of the position versus time graph
 Positive velocity means that the object is moving
in the positive direction; negative velocity means
it is moving in the negative direction.
 Speed is the magnitude of velocity, it is always
positive.
How do we express patterns
mathematically?
 An object is moving in the positive direction
at constant velocity v. It starts at clock
reading t = 0 sec, at a position x0.
 How would you write a function that will allow
you to find the position of the object at any
time?
Let’s start…
 Examine: Describe the relationship between the two
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variables.
The object changes its position by 50 meters each second
Define: Describe the variables used in the scenario
t = time elapsed
x = position
Represent: Write a mathematical equation using the
variables above (hint: how can you determine how far a car
has gone in a given amount of time?)
X = 50t
Time (seconds)
Position (meters)
1
50
2
100
3
150
Need Some Help?
 When mathematicians and physicists express
patterns mathematically they use functions.
 A function is a rule that one uses to find a
dependent variable when an independent
variable is known.
 You may have met functions in a math class.
 There the independent variable was labeled x
and the dependent variable is labeled y.
 Describe the relationship between the two
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variables.
Describe the variables used in the scenario.
Which variable is the dependent?
Which variable is the independent?
Write a mathematical equation using
variables.
How Many Velocities can an Object Have?
∆
∆
∆
What is the distance the football player traveled?
What is the displacement?
Expression for Displacement
• Devise a method for obtaining the value for
displacement and distance (path length) on a position
•
Your friend says that to find displacement, he needs
to take the position reading at point 2 and subtract
the position reading at point 1. Do you agree or
disagree?
The displacement is written:
Company
What is the Difference between Average
Speed and Velocity?
Speed: how far an object travels in a given time
interval
Velocity includes directional information:
v
x 2  x1
t 2  t1

x
t
Company
Now Draw a Velocity vs Time
Graph
Find the velocity at :
0-4 seconds
4-10 seconds
10-19 seconds
40/4= 10 yd/sec
0/6 = 0 yd/sec
-45/9 = -5 yd/sec
How do we find displacement
with velocity vs time graph?
Let’s go back to the Moving Man!
 Area under velocity curve = displacement
```