Representing MotionRepresenting MotionInvestigation 4Investigation 4

Part 1 – Complex MotionPart 1 – Complex Motion

Reviewing Graphing SpeedReviewing Graphing Speed

Slope of a distance-vs.-time graph represents Slope of a distance-vs.-time graph represents the speed of movement.the speed of movement.

Graphs can help you compare the speeds of two Graphs can help you compare the speeds of two objects. The comparison can also be used to objects. The comparison can also be used to predict when two objects going at different predict when two objects going at different speeds will meet, and how much head start one speeds will meet, and how much head start one object will need for a photo finish.object will need for a photo finish.

The graph line can be used to determine how far The graph line can be used to determine how far an object has gone after a period of time, or how an object has gone after a period of time, or how long it will take to travel a given distance.long it will take to travel a given distance.

Complex MotionComplex Motion

Most of the motion events we have been looking Most of the motion events we have been looking at are pretty simple. We investigated cars rolling at are pretty simple. We investigated cars rolling straight down ramps, races between competitors straight down ramps, races between competitors that travel at constant speeds, boats, trucks and that travel at constant speeds, boats, trucks and pogo sticks that go at steady speeds, and the pogo sticks that go at steady speeds, and the like.like.Not all motion events are simple, however. Not all motion events are simple, however. Some are pretty involved with objects traveling Some are pretty involved with objects traveling at different speeds, stopping at different places, at different speeds, stopping at different places, and going in different directions. Today we are and going in different directions. Today we are going to start looking at complex motion events.going to start looking at complex motion events.

Show Time!Show Time!

Take a look at WS 37 – Show Time ATake a look at WS 37 – Show Time A

This story describes a kind of motion we have This story describes a kind of motion we have not yet studies. The girls traveled in one not yet studies. The girls traveled in one direction to the theater and in the opposite direction to the theater and in the opposite direction back home.direction back home.

Also, just like the Iditarod race, the motion is Also, just like the Iditarod race, the motion is not continuous. There are times during the trip not continuous. There are times during the trip when the travelers are not moving.when the travelers are not moving.

Show Time A – Legs!Show Time A – Legs!

A complex motion event can be thought of as a A complex motion event can be thought of as a series of simple motion events. Simple motion series of simple motion events. Simple motion events are called events are called legslegs. A . A legleg is one easily is one easily defined part of an event.defined part of an event.

How many legs can the trip to movies be How many legs can the trip to movies be subdivided into?subdivided into?

Can you determine how fast the girls traveled Can you determine how fast the girls traveled during each leg? How?during each leg? How?

Data Table on Show Time AData Table on Show Time A

The table may help you organize the information The table may help you organize the information presented in the story.presented in the story.Column 1 is labeled “leg.” The first leg is Column 1 is labeled “leg.” The first leg is numbered 0 to remind us that just before the numbered 0 to remind us that just before the motion starts, the position is 0 km and the time is motion starts, the position is 0 km and the time is 0 minutes. 0,0 is the starting position and time.0 minutes. 0,0 is the starting position and time.Column 2 is labeled “time at end leg.” In the Column 2 is labeled “time at end leg.” In the future it will be labeled simply future it will be labeled simply tt. This is the total . This is the total elapsed time from the start of the trip (0,0) to the elapsed time from the start of the trip (0,0) to the end of each leg.end of each leg.How much time has elapsed at the end of the How much time has elapsed at the end of the first leg? At the end of the second leg?first leg? At the end of the second leg?

Column 3Column 3

Column 3 is labeled “position at end of leg.” It will be Column 3 is labeled “position at end of leg.” It will be labeled simply x, for position in the future. As time goes labeled simply x, for position in the future. As time goes along, the travelers change their position. Record along, the travelers change their position. Record where the travelers are at the end of each leg in this where the travelers are at the end of each leg in this column.column.

What is the position of the girls at the end leg 1?What is the position of the girls at the end leg 1?

At the end of leg 2?At the end of leg 2?

At the end of leg 3?At the end of leg 3?

An important ideaAn important ideaThe first part of the trip (toward the movie The first part of the trip (toward the movie house) was in the positive direction. The house) was in the positive direction. The second part of the trip (away from the second part of the trip (away from the movie house) was in the negative movie house) was in the negative direction. This will be reinforced when we direction. This will be reinforced when we get to column five – so keep that in mind.get to column five – so keep that in mind.

Column 4Column 4

Column 4 is labeled “time interval during Column 4 is labeled “time interval during leg.” In the future this column will be leg.” In the future this column will be labeled simply t. The amount of time labeled simply t. The amount of time that elapsed during the leg is recorded in that elapsed during the leg is recorded in this column. Notice that column 2 shows this column. Notice that column 2 shows the accumulated time from the start of the the accumulated time from the start of the trip; this column shows only the interval of trip; this column shows only the interval of time that passed during this leg.time that passed during this leg.What was the time interval for leg 1?What was the time interval for leg 1?

Column 5Column 5

Column 5 is labeled “displacement during leg.” Column 5 is labeled “displacement during leg.” In future activities this column will be labeled In future activities this column will be labeled simply x. Displacement is change of position simply x. Displacement is change of position and is calculated with the equation, x = xand is calculated with the equation, x = x f f -x-xii

Like position (x), change of position has both Like position (x), change of position has both magnitude and direction. When the magnitude and direction. When the displacement (change of position) is toward the displacement (change of position) is toward the movie house, x is positive. When the movie house, x is positive. When the displacement is away from the movie house, x displacement is away from the movie house, x is negative.is negative.What is the displacement in the first legWhat is the displacement in the first legThe second leg?The second leg?In the third leg?In the third leg?

Column 6Column 6

Column 6 is labeled “total distance of travel.” This is Column 6 is labeled “total distance of travel.” This is the quantity we have worked with quite a bit already. the quantity we have worked with quite a bit already. Add up how far the girls have traveled from the start of Add up how far the girls have traveled from the start of their trip to the end of each leg and record that number. their trip to the end of each leg and record that number. Distance adds up no matter which direction they move.Distance adds up no matter which direction they move.How far had the girls traveled at the end of leg 1?How far had the girls traveled at the end of leg 1?At the end of leg 2?At the end of leg 2?At the end of leg 3?At the end of leg 3?

Table – Does yours look like this?Table – Does yours look like this?

LegLeg Time at end of leg Time at end of leg

t (min.)t (min.)

Position at Position at end of leg end of leg

x (km)x (km)

Time interval Time interval during leg during leg

t (min.)t (min.)

DisplacemenDisplacement during the t during the legleg

x (km)x (km)

Total Total Distance of Distance of Travel Travel

d (km)d (km)

00 00 00

11 1010 55 1010 55 55

22 9090 55 8080 00 55

33 130130 00 4040 -5-5 1010

Plot the DataPlot the Data

When you have completed your data When you have completed your data table, generate a position-and-time graph, table, generate a position-and-time graph, not a distance-and-time graph. This is a not a distance-and-time graph. This is a position graph and it indicates where a position graph and it indicates where a moving object is at any given time, not moving object is at any given time, not how far it has traveled at any given time.how far it has traveled at any given time.In your journal tell the difference b/t the In your journal tell the difference b/t the two types of graphs.two types of graphs.Complete WS 37Complete WS 37

Reviewing the GraphsReviewing the Graphs

What was the girls’ approximate position 5 What was the girls’ approximate position 5 minutes after leaving home?minutes after leaving home?

What was their position 40 minutes after What was their position 40 minutes after leaving home? Eighty minutes after leaving home? Eighty minutes after leaving home?leaving home?

What was their approximate position 105 What was their approximate position 105 minutes after leaving home?minutes after leaving home?

Correct c, d and e…Correct c, d and e…

Reviewing PositionReviewing Position

What symbol is used to represent What symbol is used to represent position?position?What is definition of position?What is definition of position?What is a position graph?What is a position graph?What kind of information does a position What kind of information does a position graph provide?graph provide?What symbol is used to represent change What symbol is used to represent change of position?of position?How is x measured?How is x measured?

Introducing DisplacementIntroducing Displacement

What is another word for x?What is another word for x?

How are displacement and distance How are displacement and distance different?different?

Write the definition of displacement under Write the definition of displacement under Terms, Definitions and Symbols.Terms, Definitions and Symbols.

Displacement ( x) – change of position in Displacement ( x) – change of position in a direction. A moving object’s a direction. A moving object’s displacement can be positive or negative.displacement can be positive or negative.

Position GraphsPosition GraphsTake a look at Transparency 16Take a look at Transparency 16These are position graphs of motion events. These are position graphs of motion events. Let’s see if we can describe the motion Let’s see if we can describe the motion represented in each graph. represented in each graph. Let’s do the first one together…Let’s do the first one together…The object started moving at the same time the The object started moving at the same time the clock started.clock started.The object moved in the positive direction with The object moved in the positive direction with medium speed and then stopped.medium speed and then stopped.It stayed stationary for a period of time and then It stayed stationary for a period of time and then moved at high speed in the negative direction moved at high speed in the negative direction back to its starting position.back to its starting position.That’s boring – make up a story like explanation That’s boring – make up a story like explanation for each of the following graphs.for each of the following graphs.

Clancey’s AfternoonClancey’s Afternoon

WS 38-39WS 38-39

Begin by filling in the data table.Begin by filling in the data table.

We’ll correct this in about 20 minutes.We’ll correct this in about 20 minutes.

Chatting about ClanceyChatting about Clancey

How many legs did Clancey’s afternoon outing How many legs did Clancey’s afternoon outing have?have?How long was Clancey’s outing to his friends How long was Clancey’s outing to his friends house?house?How long was Clancey actually moving, on his How long was Clancey actually moving, on his way to Richie’s and on his way home?way to Richie’s and on his way home?What was the total distance Clancey traveled on What was the total distance Clancey traveled on his outing?his outing?What was the greatest distance away from home What was the greatest distance away from home that Clancey reached on his outing?that Clancey reached on his outing?Do you have enough information to determine Do you have enough information to determine Clancey’s speed during each leg of his outing?Clancey’s speed during each leg of his outing?

Motion ReviewMotion Review

Read pg. 17-19 in the Read pg. 17-19 in the Force and Motion Force and Motion book.book.

Take notes as Take notes as needed.needed.

Add any equations Add any equations into your journal that into your journal that you might need.you might need.

Part 2 – Leisurely WalksPart 2 – Leisurely Walks

What is a leisurely walk?What is a leisurely walk?

What is not a leisurely walk?What is not a leisurely walk?

Today we’re going out for some leisurely Today we’re going out for some leisurely walks. You will take the walks as a group, walks. You will take the walks as a group, keeping track of your progress as you go keeping track of your progress as you go along. There will be tasks to attend to along along. There will be tasks to attend to along the way, and data to record.the way, and data to record.

WS 41WS 41

Leisurely Walk DirectionsLeisurely Walk Directions

Each group of four students needs one Each group of four students needs one recorder. The recorder should bring their recorder. The recorder should bring their journal outside.journal outside.Each walk has more than one leg. You Each walk has more than one leg. You need to get data for each leg of the walks. need to get data for each leg of the walks. For each leg of your walks, you will record For each leg of your walks, you will record the time interval ( t) and the displacement the time interval ( t) and the displacement ( x). The last three columns t, x, and d, ( x). The last three columns t, x, and d, can be filled back in class on WS 41.can be filled back in class on WS 41.

Back in ClassBack in Class

Copy all the data from the journal onto Copy all the data from the journal onto your worksheet 41.your worksheet 41.

Make a position graph for each of your Make a position graph for each of your leisurely walks.leisurely walks.

Make Graph 1 on half of your groups white Make Graph 1 on half of your groups white board, on the other half make a distance board, on the other half make a distance graph using the same data.graph using the same data.

Repeat with Graph 2 and 3.Repeat with Graph 2 and 3.

Positive and NegativePositive and Negative

Remember, motion from the starting line Remember, motion from the starting line toward the destination line is motion in the toward the destination line is motion in the positive direction. Motion back toward the positive direction. Motion back toward the starting line is motion in the negative starting line is motion in the negative direction.direction.

Walk the walks – follow directions on your Walk the walks – follow directions on your data sheet. data sheet.

However, 40 m instead of 10 m.However, 40 m instead of 10 m.

Back in ClassBack in Class

Copy all the data from the journal onto Copy all the data from the journal onto your worksheet 41.your worksheet 41.

Make a position graph for each of your Make a position graph for each of your leisurely walks.leisurely walks.

Make Graph 1 on half of your groups white Make Graph 1 on half of your groups white board, on the other half make a distance board, on the other half make a distance graph using the same data.graph using the same data.

Repeat with Graph 2 and 3.Repeat with Graph 2 and 3.

Road Trip!Road Trip!

WS 42-43WS 42-43

Complete the table.Complete the table.

Draw a position graph for the trip.Draw a position graph for the trip.

Draw a distance graph for the trip.Draw a distance graph for the trip.

Answer the three questions on WS 43.Answer the three questions on WS 43.

Response Sheet – Representing MotionResponse Sheet – Representing Motion

Boston Treasure HuntBoston Treasure Hunt

Read pages 20-26Read pages 20-26

Answer the 3 questions on pg. 26 in your Answer the 3 questions on pg. 26 in your journal.journal.

Part 3 – Motion StoriesPart 3 – Motion Stories

WS 46 and 47WS 46 and 47These three graphs are position graphs. Each These three graphs are position graphs. Each represents a different kind of motion event.represents a different kind of motion event.Be sure to study the units of time and distance Be sure to study the units of time and distance for each graph. They are not all the same.for each graph. They are not all the same.Make up an exciting, yet appropriate story to go Make up an exciting, yet appropriate story to go with each graph. Make sure your story is with each graph. Make sure your story is reasonable. People aren’t able to run, for reasonable. People aren’t able to run, for instance, at a speed of 50 km/hinstance, at a speed of 50 km/hWrite your stories on the lines to the right of the Write your stories on the lines to the right of the graphs.graphs.

SharingSharing

Pick the best story at your table. Draw the Pick the best story at your table. Draw the graph and write the story on your white graph and write the story on your white board.board.

What four items do all of the stories have What four items do all of the stories have in common?in common?

Create a Story of Your OwnCreate a Story of Your OwnWS 47WS 47You are going to write two stories that one person at You are going to write two stories that one person at your table can interpret and represent as a graph. your table can interpret and represent as a graph. One person will do one story, a second person at the One person will do one story, a second person at the table will do the second story.table will do the second story.Start in your journal first, then once you’re sure Start in your journal first, then once you’re sure everything is going to work, transcribe it onto the everything is going to work, transcribe it onto the worksheet. worksheet. So you’ll have two copies of your stories, one in your So you’ll have two copies of your stories, one in your journal, and one on the WSjournal, and one on the WSMake sure your name is on both sides of your WS.Make sure your name is on both sides of your WS.If the story you are interpreting does not have enough If the story you are interpreting does not have enough information – consult with the author! Have them fix it!information – consult with the author! Have them fix it!Turn in your WS for credit.Turn in your WS for credit.

Riding on Springer HillRiding on Springer Hill

Open your books to Open your books to page 27.page 27.

Read pg. 27-31.Read pg. 27-31.

Answer the 5 questions Answer the 5 questions on pg. 31 in your journal.on pg. 31 in your journal.

Graph Motion with MultimediaGraph Motion with Multimedia

Computer disc time!Computer disc time!

The Motion Stories The Motion Stories program has two program has two activities: Graph a activities: Graph a Story and Choose a Story and Choose a Story. Try both Story. Try both activities.activities.

Multimedia cont.Multimedia cont.

Graph a Story starts with a story. Make a Graph a Story starts with a story. Make a position graph that represents the motion position graph that represents the motion in a story.in a story.Choose a story starts with a graph of a Choose a story starts with a graph of a motion event. Analyze each leg of the motion event. Analyze each leg of the motion and select a sentence that best motion and select a sentence that best describes that motion. The selected describes that motion. The selected sentences should make a story that sentences should make a story that describes the motion represented by the describes the motion represented by the graph.graph.

And Tomorrow or Whenever…And Tomorrow or Whenever…

Assessment 4Assessment 4