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 = x f -x i 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.) t (min.) Displacemen t during the leg x (km) x (km) Total Distance of Travel d (km)

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 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 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 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 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 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