Transcript Representing Motion Investigation 4 Part 1 – Complex Motion Reviewing Graphing Speed Slope of a distance-vs.-time graph represents the speed of movement. Graphs can.

Representing Motion
Investigation 4
Part 1 – Complex Motion
Reviewing Graphing Speed
Slope of a distance-vs.-time graph represents
the speed of movement.
Graphs can help you compare the speeds of two
objects. The comparison can also be used to
predict when two objects going at different
speeds will meet, and how much head start one
object will need for a photo finish.
The graph line can be used to determine how far
an object has gone after a period of time, or how
long it will take to travel a given distance.
Complex Motion
Most of the motion events we have been looking
at are pretty simple. We investigated cars rolling
straight down ramps, races between competitors
that travel at constant speeds, boats, trucks and
pogo sticks that go at steady speeds, and the
like.
Not all motion events are simple, however.
Some are pretty involved with objects traveling
at different speeds, stopping at different places,
and going in different directions. Today we are
going to start looking at complex motion events.
Show Time!
Take a look at WS 37 – Show Time A
This story describes a kind of motion we have
not yet studies. The girls traveled in one
direction to the theater and in the opposite
direction back home.
Also, just like the Iditarod race, the motion is
not continuous. There are times during the trip
when the travelers are not moving.
Show Time A – Legs!
A complex motion event can be thought of as a
series of simple motion events. Simple motion
events are called legs. A leg is one easily
defined part of an event.
How many legs can the trip to movies be
subdivided into?
Can you determine how fast the girls traveled
during each leg? How?
Data Table on Show Time A
The table may help you organize the information
presented in the story.
Column 1 is labeled “leg.” The first leg is
numbered 0 to remind us that just before the
motion starts, the position is 0 km and the time is
0 minutes. 0,0 is the starting position and time.
Column 2 is labeled “time at end leg.” In the
future it will be labeled simply t. This is the total
elapsed time from the start of the trip (0,0) to the
end of each leg.
How much time has elapsed at the end of the
first leg? At the end of the second leg?
Column 3
Column 3 is labeled “position at end of leg.” It will be
labeled simply x, for position in the future. As time goes
along, the travelers change their position. Record
where the travelers are at the end of each leg in this
column.
What is the position of the girls at the end leg 1?
At the end of leg 2?
At the end of leg 3?
An important idea
The first part of the trip (toward the movie
house) was in the positive direction. The
second part of the trip (away from the
movie house) was in the negative
direction. This will be reinforced when we
get to column five – so keep that in mind.
Column 4
Column 4 is labeled “time interval during
leg.” In the future this column will be
labeled simply t. The amount of time
that elapsed during the leg is recorded in
this column. Notice that column 2 shows
the accumulated time from the start of the
trip; this column shows only the interval of
time that passed during this leg.
What was the time interval for leg 1?
Column 5
Column 5 is labeled “displacement during leg.”
In future activities this column will be labeled
simply x. Displacement is change of position
and is calculated with the equation, x = xf -xi
Like position (x), change of position has both
magnitude and direction. When the
displacement (change of position) is toward the
movie house, x is positive. When the
displacement is away from the movie house, x
is negative.
What is the displacement in the first leg
The second leg?
In the third leg?
Column 6
Column 6 is labeled “total distance of travel.” This is
the quantity we have worked with quite a bit already.
Add up how far the girls have traveled from the start of
their trip to the end of each leg and record that number.
Distance adds up no matter which direction they move.
How far had the girls traveled at the end of leg 1?
At the end of leg 2?
At the end of leg 3?
Table – Does yours look like this?
Leg
Time at end of leg
t (min.)
Position at
end of leg
x (km)
Time interval
during leg
t (min.)
Displacemen
t during the
leg
x (km)
Total
Distance of
Travel
d (km)
0
0
0
1
10
5
10
5
5
2
90
5
80
0
5
3
130
0
40
-5
10
Plot the Data
When you have completed your data
table, generate a position-and-time graph,
not a distance-and-time graph. This is a
position graph and it indicates where a
moving object is at any given time, not
how far it has traveled at any given time.
In your journal tell the difference b/t the
two types of graphs.
Complete WS 37
Reviewing the Graphs
What was the girls’ approximate position 5
minutes after leaving home?
What was their position 40 minutes after
leaving home? Eighty minutes after
leaving home?
What was their approximate position 105
minutes after leaving home?
Correct c, d and e…
Reviewing Position
What symbol is used to represent
position?
What is definition of position?
What is a position graph?
What kind of information does a position
graph provide?
What symbol is used to represent change
of position?
How is x measured?
Introducing Displacement
What is another word for x?
How are displacement and distance
different?
Write the definition of displacement under
Terms, Definitions and Symbols.
Displacement ( x) – change of position in
a direction. A moving object’s
displacement can be positive or negative.
Position Graphs
Take a look at Transparency 16
These are position graphs of motion events.
Let’s see if we can describe the motion
represented in each graph.
Let’s do the first one together…
The object started moving at the same time the
clock started.
The object moved in the positive direction with
medium speed and then stopped.
It stayed stationary for a period of time and then
moved at high speed in the negative direction
back to its starting position.
That’s boring – make up a story like explanation
for each of the following graphs.
Clancey’s Afternoon
WS 38-39
Begin by filling in the data table.
We’ll correct this in about 20 minutes.
Chatting about Clancey
How many legs did Clancey’s afternoon outing
have?
How long was Clancey’s outing to his friends
house?
How long was Clancey actually moving, on his
way to Richie’s and on his way home?
What was the total distance Clancey traveled on
his outing?
What was the greatest distance away from home
that Clancey reached on his outing?
Do you have enough information to determine
Clancey’s speed during each leg of his outing?
Motion Review
Read pg. 17-19 in the
Force and Motion
book.
Take notes as
needed.
Add any equations
into your journal that
you might need.
Part 2 – Leisurely Walks
What is a leisurely walk?
What is not a leisurely walk?
Today we’re going out for some leisurely
walks. You will take the walks as a group,
keeping track of your progress as you go
along. There will be tasks to attend to along
the way, and data to record.
WS 41
Leisurely Walk Directions
Each group of four students needs one
recorder. The recorder should bring their
journal outside.
Each walk has more than one leg. You
need to get data for each leg of the walks.
For each leg of your walks, you will record
the time interval ( t) and the displacement
( x). The last three columns t, x, and d,
can be filled back in class on WS 41.
Back in Class
Copy all the data from the journal onto
your worksheet 41.
Make a position graph for each of your
leisurely walks.
Make Graph 1 on half of your groups white
board, on the other half make a distance
graph using the same data.
Repeat with Graph 2 and 3.
Positive and Negative
Remember, motion from the starting line
toward the destination line is motion in the
positive direction. Motion back toward the
starting line is motion in the negative
direction.
Walk the walks – follow directions on your
data sheet.
However, 40 m instead of 10 m.
Back in Class
Copy all the data from the journal onto
your worksheet 41.
Make a position graph for each of your
leisurely walks.
Make Graph 1 on half of your groups white
board, on the other half make a distance
graph using the same data.
Repeat with Graph 2 and 3.
Road Trip!
WS 42-43
Complete the table.
Draw a position graph for the trip.
Draw a distance graph for the trip.
Answer the three questions on WS 43.
Response Sheet – Representing Motion
Boston Treasure Hunt
Read pages 20-26
Answer the 3 questions on pg. 26 in your
journal.
Part 3 – Motion Stories
WS 46 and 47
These three graphs are position graphs. Each
represents a different kind of motion event.
Be sure to study the units of time and distance
for each graph. They are not all the same.
Make up an exciting, yet appropriate story to go
with each graph. Make sure your story is
reasonable. People aren’t able to run, for
instance, at a speed of 50 km/h
Write your stories on the lines to the right of the
graphs.
Sharing
Pick the best story at your table. Draw the
graph and write the story on your white
board.
What four items do all of the stories have
in common?
Create a Story of Your Own
WS 47
You are going to write two stories that one person at
your table can interpret and represent as a graph.
One person will do one story, a second person at the
table will do the second story.
Start in your journal first, then once you’re sure
everything is going to work, transcribe it onto the
worksheet.
So you’ll have two copies of your stories, one in your
journal, and one on the WS
Make sure your name is on both sides of your WS.
If the story you are interpreting does not have enough
information – consult with the author! Have them fix it!
Turn in your WS for credit.
Riding on Springer Hill
Open your books to
page 27.
Read pg. 27-31.
Answer the 5 questions
on pg. 31 in your journal.
Graph Motion with Multimedia
Computer disc time!
The Motion Stories
program has two
activities: Graph a
Story and Choose a
Story. Try both
activities.
Multimedia cont.
Graph a Story starts with a story. Make a
position graph that represents the motion
in a story.
Choose a story starts with a graph of a
motion event. Analyze each leg of the
motion and select a sentence that best
describes that motion. The selected
sentences should make a story that
describes the motion represented by the
graph.
And Tomorrow or Whenever…
Assessment 4