1 Unit: Graphing Motion Objectives: Describe types of straight line motion. Design experiments to collect data and analyze motion. Use graphs to describe

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Unit: Graphing MotionObjectives: Describe types of straight line motion.Design experiments to collect data and analyze motion.Use graphs to describe the motion of the object.

Book Assignment:Physics A: Reading 2.7 and Appendix C

Physics Honors: Read 2.8 Question #s 17 and 19Problem #s 51 - 59

Work with the person next to you, create a list of different types of linear (straight line) motion.

What is acceleration vs. velocity?

2

Work with the person next to you, create a list of different types of linear (straight line) motion.

Compare acceleration to velocity

3

Demonstrations:

Constant Velocity

Bowling ball rolling on floorAir Hockey PuckWhat role does friction play in these?

Sketch graphs of the motion on the axes below.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Time (seconds)

Time (seconds) Time (seconds)

Displacement

(m)

Velocity

(m/s)

Acceleration

(m/s2)

4

Constant Acceleration

Bowling Ball rolling down a rampDropping a book above a tableDropping a sheet of paper uncrumpled vs. crumpledWhat role does friction play in these?


0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Time (seconds)


Displacement

(m)

Velocity

(m/s)

Acceleration

(m/s2)

5

Air Resistance: Drafting

6

Constant Deceleration

Bowling Ball rolling up a rampPushing cart across floor - roll to a stopBook sliding to rest on a tableWhat role does friction play in these?


0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Time (seconds)


Displacement

(m)

Velocity

(m/s)

Acceleration

(m/s2)

7

Activity: Graphing the Motion of a Toy Buggy

Observe the buggy. What type of motion is this?What role does friction play in this case?

8

Buggy Rules:1. Cheap and Fragile2. Don’t drop it.3. Don’t push it with the motor off.4. Don’t restrain the buggy from motion.

Objective:1. In a group of 4, collect displacement/time data and graph

it. You should have at least four data points.2. Determine the actual velocity of the buggy.

Materials:1. Buggy2. Stop Watches3. Meter Sticks4. Graph paper or computer

9

General Lab Conduct: THESE APPLY ALL YEAR!1. Treat others with respect.2. If you put any marks on the floor, remove them.3. When in the hall, be respectful of other classes.4. Clean up all materials - leave the room in better condition

than you found it.5. Failure to follow these rules will result in boring lab lectures

instead of activities.

Any questions?You may begin. As you are collecting your data, on a separate piece of paper, create a data table, a sketch of your set-up and a brief description of the procedure. Then we can process the data before graphing.

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What is good data?1. As many data points as reasonable.2. A set of data points is for a given run of the buggy.3. Be consistent with measurements, ie always use the same

spot on the object. 4. Appropriate units.5. Correct experimental design.

For example, a rolling start in this case.6. Consider sources of error - avoidable ones vs. unavoidable

ones.7. Why was it easier to set the distance and measure the time?

11

Refer to Handout: Steps for Creating a Graph in Excel

Steps for Creating a Graph in Excel

1. Open the Lab Program Excel.2. Enter your data in the columns. Column A will be your X axis and Column B and beyond will

be your Y axis (if you have more than one line on the graph). If you label the top of column Betc., Excel will make a correct legend for your graph. Do not label column A.

3. Select your data columns.4. Click and drag down the INSERT menu and select CHART.5. Select the X-Y Scatter Chart and then Next in the chart type box.6. Click Next in Chart Source Data (Step 2 of 4).7. Chart Options Menu: (1) Titles – enter a title for the graph [X Axis Title vs. Y Axis Title] Be

sure to include UNITS; (2) Gridlines: Check all major and minor gridlines; (3) Legend: clickoff legend. (Step 3 of 4)

8. ALWAYS choose As New Sheet from menu and click Finish. (Step 4 of 4)9. Right click on any data point on your graph, then left click on Add Trendline.10. Click on linear line for linear data or 2nd degree polynomial for parabolic data. Note: do not

exit this box: instead, open the other card, Options.11. Click on set y-intercept 0 if your graph should go through the origin. You may also

extrapolate in front of or beyond your data points. You may also display the equation of yourcurve on your graph. Click OK. Drag the equation to the top of your graph.

12. Right click on graph and choose Format Plot Area. Under Area – choose WHITE and clickOK.

13. Click on the printer icon on the toolbar.

12

Add the following steps to this handout.

Making a good graph:1. Start with the end in mind (have an idea of what the graph

should look like).2. Make sure the scale/numbers is/are appropriate - data takes

up at least 3/4 of the graph.3. Label all axes with titles and units.4. Title graph (Y Title vs. X Title).5. Do not connect the data points. Draw a trend line.6. In an Excel graph, make sure the background is white!7. Be sure to put your name in the header,footer or text box.8. In the Excel graph, turn on major and minor gridlines.

Follow these rules and create a graph of your data.

13

Here is a graph of some sample dataDisplacement vs. Time For a Toy Buggy

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

Time (seconds)

Displacement (meters)

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Did you draw a trendline?Did you label the axes?In Physics class, the units are as important as the numbers.

SLOPE = RISE/RUN What is the rise?

METERSWhat is the run?

SECONDSWhat is the rise/run?

METERS/SECONDDoes this have any physical meaning for this graph? (What is

this a measurement of?)VELOCITY

This method of unit analysis works for any graph to see what the graph is measuring.

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What are some shapes that you can calculate the area of?Rectangle = base x height, Triangle = 1/2 base x height

Look at your graph, do you see a triangle?What are the units of the base?

SECONDSWhat are the units of the height?

METERSWhat would the units of the area of this triangle be?

SECONDS x METERSDoes the area under the line have any physical meaning?

Not in this graph, but it may depending on the graph.

You should always check the slope and area of any graph to see if they have any physical meaning.

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When calculating slope, you should always use points that arefar enough apart to be accurate.

Steps for Calculating Slope:1. Determine the numerical value of each division on the X and

Y axes. Remembering that each box does not necessarily equal one unit.

2. Select two points that are far apart on your line. These are not actual data points, because data points rarely fall on the trendline.

3. Carefully label their X,Y coordinates.4. Determine slope using change in Y over change in X. Don’t

forget the UNITS and SHOW ALL WORK!5. Just for fun, convert your slope to miles/hour.

The next slide will show you what your graph should look like.Who had the fastest vehicle in the class?

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Displacement vs. Time For a Toy Buggy

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

Time (seconds)


(5.6,1.52

(2.2,0.6)

run

rise

€

Slope =rise

run=change in y

change in x=

ΔY

ΔX=

1.52 − 0.6

5.6 − 2.2=

0.92 meters

3.4 seconds= 0.27

meters

second

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Pick three points on your displacement time graph and determine the velocity at those points. You should pick points: one in the beginning, one in the middle and one at the end of the run.

Create a data table on your graph of these times and velocities.

19

Displacement vs. Time For a Toy Buggy

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

Time (seconds)


(5.6,1.52

(2.2,0.6)

run

rise

€

Slope =rise

run=change in y

change in x=

ΔY

ΔX=

1.52 − 0.6

5.6 − 2.2=

0.92 meters

3.4 seconds= 0.27

meters

second

Time (seconds)

Velocity(meters/sec)

1 0.27

3 0.27

5 0.27

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Create a graph of velocity vs. time using the data table from the displacement time graph.

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Velocity vs. Time For a Toy Buggy

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6

Time (seconds)

Velocity (meters/second)

22

SLOPE = RISE/RUN What is the rise?

METERS/SECONDWhat is the run?

SECONDSWhat is the rise/run?

METERS/SECOND/SECOND = METERS/SECOND2

Does this have any physical meaning for this graph? (What is this a measurement of?)ACCELERATION

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Here are a few questions about acceleration:

What does acceleration tell you about the motion of the object?It tells you how fast the velocity is changing and if the object is speeding up or slowing down.

Describe how you would feel in your car if you were undergoing a rapid acceleration.

What would happen to a cup of coffee on your dash board?The cup of coffee would slide off of the dash board towardthe back of the car.

Does the cup of coffee ever really move backwards relative to the road?No. See the following video clip of Richard Feynman(Nobel Prize Physics 1965) discussing a similar situation.

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25

Describe how you would feel in your car if you were undergoing a rapid deceleration.

What would happen to a cup of coffee on your dash board?The cup of coffee would slide into the windshield.

Watch the following demonstration with a rolling cart and amass on the rolling cart.

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0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6

Time (seconds)


27

What shape is between the line and the X axis (under the line)?RECTANGLE

What are the units of the base?SECONDS

What are the units of the height?METERS/SECOND

What would the units of the area of this rectangle be?METERS

Does the area under the line have any physical meaning?Yes, displacement.

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0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6

Time (seconds)


What is the velocity at 2 seconds?0.27 m/s

You obtain this by reading directly off the graph.

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0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6

Time (seconds)


What is the acceleration at 2 seconds?To obtain the answer, calculate the slope of the line.Pick two points far apart on the graph.

€

Slope =rise

run=change in y

change in x=

ΔY

ΔX=

0.27 − 0.27

5.4 − 0.4=

0 meters /second

5.0 seconds= 0

meters

second2

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0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6

Time (seconds)


What is the displacement between 2 and 4 seconds?To obtain the answer, calculate the area under the line.

€

Area of the shaded box = base x height

base = 4s− 2s = 2s

height = 0.27m /s− 0m /s = 0.27m /s

Area = 2s x 0.27m /s = 0.54m

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Pick three points on your velocity time graph and determine the acceleration at those points. You should pick points: one in the beginning, one in the middle and one at the end of the run.

Create a data table on your velocity time graph of these times and accelerations.

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0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6

Time (seconds)


To obtain the answer, calculate the slope of the line.Pick two points far apart on the graph.

€

Slope =rise

run=change in y

change in x=

ΔY

ΔX=

0.27 − 0.27

5.4 − 0.4=

0 meters /second

5.0 seconds= 0

meters

second2

Use this data table to create an acceleration time graph.

Time (seconds)

Accel(m/s^2)

1 0

3 0

5 0

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Acceleration vs. Time For a Toy Buggy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6

Time (seconds)

Acceleration (m/s^2)

What does this graph tell us about the velocity of the buggy?The velocity is not changing, but we don’t know what the velocity is.

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What would an acceleration time graph look like if the buggy wasn’t turned on?The graph would look the same.

What would an acceleration time graph look like of a car on cruise control driving down a straight road?The graph would look the same.

The point is that sitting still or going fast will look the same onan acceleration time graph as long as the velocity is not changing.

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Type of Graph

Read the Graph

Calculate the Slope

Calculate the Area

Displacement vs. Time

Displacement (m)

Velocity (m/s)

Nothing (ms)

Velocity vs. Time

Velocity (m/s)

Change in Velocity

or Accelerati

on (m/s/s or

m/s2)Δ Velocity

Displacement (m)

Acceleration vs. Time

Acceleration

(m/s/s or m/s2)

Change in Accelerati

on(m/s/s/s

or m/s2/s or m/s3)Δ

Acceleration

Velocity(m/s)

Put this table in your notes or on the back of your directions for Graphing in Excel!

36

To complete the Toy Buggy Activity, you should have the following:

Page 1: Sketch, raw data and description of procedure.Page 2: Displacement vs. Time Graph with associated

work.Page 3: Velocity vs. Time Graph with associated work.Page 4: Acceleration vs. Time GraphPage 5: Toy Buggy Worksheet (see next slide)

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Name ____________________________ Date ____________

Questions for Graphs of Constant Velocity Motion: Toy Buggy ActivityBE SURE TO SHOW WORK OR EXPLAIN YOUR ANSWER!!!!!!!!!You cannot use the EXCEL Equation to answer the questions.

1) Using the displacement vs. time graph, how far did the buggy go between 0seconds and 5 seconds?

2) Using the displacement vs. time graph, what is the instantaneous velocity at 2seconds?

3) Using the displacement vs. time graph, what is average velocity between 2seconds and 5 seconds?

4) Using the velocity vs. time graph, how far did the buggy go between 1 second and3 seconds?

5) Using the displacement vs. time graph, how far did the buggy go between 2 and 3seconds?

6) Using the velocity vs. time graph, how long would it take for the buggy to travel 2meters?

7) Using the velocity vs. time graph, what is the acceleration at time equal to 3seconds?

8) What does the acceleration vs. time graph tell you about the motion of the buggy?i.e Does it have to be moving based on this graph?

9) Using the acceleration vs. time graph, what is the acceleration at time equal to 2seconds?

10) How long will it take for this object to double it's speed?

11) Give an example of an object that travels at a constant speed but has changingvelocity.

12) How can you tell this set of graphs were for an object moving at a constantvelocity? Give evidence from each of the three graphs.

13) Draw a Free Body Diagram (Force Diagram) for the buggy moving across thefloor.

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0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Time (seconds)


Displacement

(m)

Velocity

(m/s)

Acceleration

(m/s2)

Demonstration: Roll bowling ball across the floor.After the bowling ball is released, describe it’s motion. Sketch this motion on the three axes below.Assuming the bowling ball leaves my hand at 1 m/s, how much distance will it cover in the first second of travel compared with the last second of travel?

Should be 1 m for both times.On the same axes in a different color, sketch the bowling ball rolling at a constant speed of 2m/s.Compare the lines on each graph.

39

Now let’s talk about accelerated motion (velocity is changing).Demonstration: Roll bowling ball from rest down ramp.Describe the velocity as the ball rolls down the ramp.

The velocity increases.How is velocity represented on a displacement time graph?

The steepness (slope) of the line.So what must happen to the slope on a displacement time graphfor the bowling ball rolling down the ramp?

The slope becomes steeper as time goes on.Sketch the graphs below. Explain your lines to your neighbor.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Time (seconds)


Displacement

(m)

Velocity

(m/s)

Acceleration

(m/s2)

40

41

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Time (seconds)


Displacement

(m)

Velocity

(m/s)

Acceleration

(m/s2)

Most of you have heard the term free fall, what do you think itmeans?Demonstration: Drop book and paper.Which one of these is in free fall?

The book. Air resistance is counteracting gravity on the paper so the paper is not free to just fall.

What could we do to the paper to help it fall more freely?Crumple it up.

On the three axes below, sketch graphs for the book falling assuming it is a constant acceleration.

42

Assuming no air resistance, what is the constant acceleration of gravity near the surface of the earth?

9.8 m/s2, but it is ok to use 10 m/s2 except when dealing with data. Galileo measured this concept of acceleration, using ramps to slow the effect of gravity, and bells to measure where the ball was.

Let’s talk about what this means, an acceleration of 10 m/s2 is means that the speed of a freely falling object changes by 10 m/s every second. Lets Review

€

Slope =rise

run=change in y

change in x=

ΔY

ΔX=

10 − 0

1− 0=

10 meters /second

1 second=10

meters

second2

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Assuming no air resistance, what is the constant acceleration of gravity near the surface of the earth?

9.8 m/s2, but it is ok to use 10 m/s2 except when dealing with data. Galileo measured this concept of

acceleration, using ramps to slow the effect of gravity, and bells to measure where the ball was.

Galileos FingerGalileo's Ramp

Let’s talk about what this means, an acceleration of 10 m/s2

means that the speed of a freely falling object changes by 10 m/s every second. Lets Review

€

Slope =rise

run=change in y

change in x=

ΔY

ΔX=

10 − 0

1− 0=

10 meters /second

1 second=10

meters

second2

http://www2.jpl.nasa.gov/galileo/finger.html

http://brunelleschi.imss.fi.it/museum/esim.asp?c=404013

44

Let’s look at some sample data for an object in free fall dropped from rest. Time

(s)

Velocity

(m/s)

0 0

1 10

2 20

3 30

4 40

How does this data represent constant acceleration?The change in velocity per second is always 10 m/s.

Time

(s)

Velocity

(m/s)

0 0

1 10

2 20

3 30

4 40

10 m/s

10 m/s

10 m/s

10 m/s

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The idea of constant acceleration has some important consequences on your graphs.

The main one is that your velocity time graphs must be straight lines.

Why is this true?The slope of the velocity time graph is acceleration and therefore can only have one numeric value.

The second consequence is that your acceleration time graphs must be horizontal straight lines.

46

Now let’s analyze the motion of the bowling ball rolling down a ramp more accurately.

Do you think this will be constant acceleration like the book in free fall?

How will this experiment’s start compare with the start of the Toy Buggy Experiment?

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Objective: Organize as a class and collect displacement time data. Refer to your notes for collecting good data and make surethat you have at least five data points.

Materials:• Bowling Ball• Wooden Ramp• Stop Watches• Meter Sticks• Graph paper or computer

Any questions?You may begin. As you are collecting your data, on a separate piece of paper, create a data table, a sketch of your set-up and a brief description of the procedure. Then we can process the data before graphing.

48

For review: What is good data?1. As many data points as reasonable.2. A set of data points is for a given roll of the bowling ball.3. Be consistent with measurements, ie always use the same

spot on the object. 4. Appropriate units.5. Correct experimental design.

For example, a stationary start in this case.6. Consider sources of error - avoidable ones vs. unavoidable

ones.7. Why was it easier to set the distance and measure the time?

49

What do you think the shape of the line will be on the displacement time graph?

Curved upward because the velocity increases and thereforethe slope of the line increases.

Plot your data, but do not draw a trendline yet.Can you see a curved upward line?Are there any points that seem like they don’t fit? These are called outliers.

50

Here is some sample data of an actual dataDisplacement vs. Time For a Accelerating Bowling Ball

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (seconds)


51

Complete the graph by adding a trendline. See the Excel Handout for details. If you are using Excel, make sure you fit the points with a second order polynomial. This is a fancy way of saying that the line has one curve.

Displacement vs. Time For a Accelerating Bowling Bally = 0.1789x2 + 0.0453x - 0.0004

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (seconds)


52

Pick three points on your displacement time graph and determine the velocity at those points. You should pick points: one in the beginning, one in the middle and one at the end of the run.

How is this process going to differ compared to the constant velocity buggy?

You need to take the slope at the points of interest because the slope changes.

53

Draw tangent lines at your points of interest.Displacement vs. Time For a Accelerating Bowling Ball

y = 0.1789x2 + 0.0453x - 0.0004

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (seconds)


Medium time, 2.5s, tangent line was drawn. Your time might vary.

54

Pick two points on the tangent line and determine the slopeDisplacement vs. Time For a Accelerating Bowling Ball

y = 0.1789x2 + 0.0453x - 0.0004

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (seconds)


(2.7,1.4)

(4.6,3.2)

€

Slope =ΔY

ΔX=

3.2 −1.4

4.6 − 2.7=

1.8 meters

1.9 seconds= 0.95

meters

second

55

This means is that at 2.5 s the bowling ball was traveling at 0.95 m/s.Look at the velocity (slope) of the line before 2.5 s. How do you think it will compare to the velocity you just found?

The velocity will be less than 0.95 m/s.Look at the velocity (slope) of the line after 2.5 s. How do you think it will compare to the velocity you just found?

The velocity will be more than 0.95 m/s.Pick a time before 2.5 s, draw a tangent line and calculate thevelocity.Pick a time after 2.5 s, draw a tangent line and calculate thevelocity.

Warning: Do not pick points to close to the beginning or end of your curve or you will not be able to draw a tangent line. Warning: Do not pick your original data points because they are not part of the trendline.

56

Here is a sample graph with all work shown for all three velocities.

57

Create a graph of velocity vs. time using the data table from the displacement time graph. It should look like this:

Velocity vs. Time For a Accelerating Bowling Ball

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (seconds)

Velocity (m/s)

58

What will the slope of this line tell us?Acceleration.

You need to graph acceleration vs. time. How will you do it?Find the slope of the trendline. Do not use your data points. Select two points, one at the beginning and one at the end, on your trendline.

59


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (seconds)

Velocity (m/s)

Time

(s)

Accel

(m/s^2)

0 0.37

1 0.37

2.5 0.37

4 0.37

€

Slope =ΔY

ΔX=

1.2 − 0.2

3.2 − 0.5=

1.0 meter /second

2.7 seconds= 0.37

meters

second2

(3.2, 1.2)

(0.5, 0.2)

60

Use this data table to create an acceleration time graph.Acceleration vs. Time For a Accelerating Bowling Ball

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (seconds)

Acceleration (m/s^2)

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What is the velocity at 2 seconds?0.76 m/s

You obtain this by reading directly off the graph.Velocity vs. Time For a Accelerating Bowling Ball

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Velocity (m/s)

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What is the acceleration at 2 seconds?To obtain the answer, calculate the slope of the line.Pick two points far apart on the graph.


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Time (seconds)

Velocity (m/s)

€

Slope =ΔY

ΔX=

1.2 − 0.2

3.2 − 0.5=

1.0 meter /second

2.7 seconds= 0.37

meters

second2

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What is the displacement between 1 and 3 seconds?To obtain the answer, calculate the area under the line.

€

Area of the triangle + Area of the rectangle = (1

2 x base x height) + (base x height)

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2x 2sec x 0.72

m

s

⎛

⎝ ⎜

⎞

⎠ ⎟+ 2sec x 0.4

m

s

⎛

⎝ ⎜

⎞

⎠ ⎟= 1.52 m


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Time (seconds)

Velocity (m/s)

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To complete the Bowling Ball Activity, you should have the following:

Page 1: Sketch, raw data and description of procedure.Page 2: Displacement vs. Time Graph with associated

work.Page 3: Velocity vs. Time Graph with associated work.Page 4: Acceleration vs. Time GraphPage 5: Bowling Ball Worksheet (see next slide)

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Name ____________________________ Date ____________

Questions for Graphs of Constant Acceleration Motion: Bowling Ball ActivityBE SURE TO SHOW WORK OR EXPLAIN YOUR ANSWER!!!!!!!!!You cannot use the EXCEL Equation to answer the questions.

1) Using the displacement vs. time graph, how far did the bowling ball go after ithad traveled for 3 seconds?

2) Using the displacement vs. time graph, what is the instantaneous velocity at 2seconds

3) Using the displacement vs. time graph, what is average velocity between1seconds and 3 seconds?

4) Using the velocity vs. time graph, how far did the ball travel between 1 secondand 3 seconds?

5) Using the displacement vs. time graph, how far did the ball travel between 2 and 3seconds?

6) Using the velocity vs. time graph, how far did the ball travel between 1 and 2seconds?

7) Using the velocity vs. time graph, what is the acceleration of the ball at time equalto 3 seconds?

8) What does the acceleration vs. time graph tell you about the motion of the ball?i.e Does it have to be moving based on this graph?

9) Using the acceleration vs. time graph, what is the acceleration at time equal to 2seconds?

10) Using the acceleration vs. time graph, what is the gain in velocity between 2 and 3seconds?

11) Give an example of an object that is accelerating but traveling at a constant speed.

12) How can you tell these graphs were constructed for an object undergoing aconstant acceleration? Give evidence from each of the three graphs.

13) What conditions must be present for an object to undergo a constant acceleration?

14) Draw a Free Body Diagram (Force Diagram) for the ball rolling down the ramp.

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The Bike Lab

Objective: To design and execute experiments that demonstrateconstant velocity, constant acceleration and constantdeceleration. Create the motion graphs and answer questions that analyze the motion.

Materials:1. Bike2. Helmet3. Stop Watches4. Tape Measure5. Chalk

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Your instructor will break the class into three groups. Each group is responsible for designing an experiment for one of the types of motion that includes jobs for everyone in the class. The class will collect data together. The data will be graphed and analyzed in groups of two.

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To complete the Bike Lab, you should have the following:

1. Sketch, raw data and description of procedure for each type of motion on a separate page.

2. Displacement vs. Time Graph with associated work foreach type of motion on a separate page.

3. Velocity vs. Time Graph with associated work for each type of motion on a separate page.

4. Acceleration vs. Time Graph for each type of motion on a separate page. Note: Deceleration is just a negative acceleration.

5. Bike Lab Worksheet (see next slide)

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Assemble the finished Bike Lab according to your instructor’s directions.

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Assemble the finished Bike Lab in the following order!

Graph 1A – Displacement vs. Time for Constant Velocity BikeGraph 1B – Velocity vs. Time for Constant Velocity Bike Graph 1C – Acceleration vs. Time for Constant Velocity BikeGraph 2A – Displacement vs. Time for Constant Acceleration BikeGraph 2B – Velocity vs. Time for Constant Acceleration Bike Graph 2C – Acceleration vs. Time for Constant Acceleration BikeGraph 3A – Displacement vs. Time for Constant Deceleration BikeGraph 3B – Velocity vs. Time for Constant Deceleration Bike Graph 3C – Acceleration vs. Time for Constant Deceleration BikeAnswers to Bike Activity Worksheet showing all formulas and work on graphs.

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You now have everything you need to complete the worksheetPacket. Complete it! Physics is not a spectator sport…

Additional ResourcesPhysics Education Technology WebsiteThe main site can be found at http://phet.colorado.eduMoving Man JAVA Applet

http://phet.colorado.edu/

http://phet.colorado.edu/new/simulations/sims.php?sim=The_Moving_Man

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Looking at the graphs of the bowling ball on the ramp or the bikeon the hill, what is important about the acceleration?

It is constant, like free fall.If acceleration is constant, the velocity changes by equal increments every second.As a ball falls, how much does its velocity change by each second?

10 m/s every second.Now imagine riding in a car with a stick shift as someone shifts through the gears, how do you feel?Would it feel the same as if you were the ball falling?How are these motions different?Things in nature rarely have constant acceleration.This means that acceleration is changing every second.

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Hills on ski slopes are good examples of non-constant acceleration.

Imagine skiing down these hills below, sketch an accelerationvs. time graph for each. Keep in mind, free fall has an acceleration of 10 m/s2 and a flat surface has an acceleration of 0 m/s2.

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Line at Line start Line start at less than higher than last 0 m/s2, rise to 10 m/s2. and end 0 m/s2. less than 10m/s2. Last two graphs have lines that are not really straight.

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If velocity changes for an object in motion, we say that the object is undergoing acceleration.When acceleration changes in your car, you often jerk forwardor backward. If acceleration changes for an object in motion, we say that the object is undergoing jerks.

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Activity: Graphing the Motion of a Real Car

Get some real dataTry this http://www.car-videos.com/performanceor any other source

Complete the worksheet on Real Car MotionPhysics Name ___________________________ # ___Real Car Motion Period ______ Date ____________________

http://www.car-videos.com/performance / or any other sourceSelect a vehicle and attach a printout of the data to this sheet

1) Obtain velocity vs. time data for a real car from a magazine or on-line. Convert to m/s.1 mile= 1609 metersShow at least one sample conversion with unit cancelation

Time(Seconds)Velocity(miles/hour) Velocity(meters/second)

2) Graph the data. Does this car experience constant acceleration? Show evidence on yourgraph. You may have to use a polynomial higher than 2 when you insert the trend line.Attach this graph

3) What was the acceleration at t = 5 seconds? show work on your graph, label it #3

4) How far did the car travel after 10 seconds? Answer in miles and metersshow work on your graph, label it #4

5) Why does the curve flatten out as time increases?

http://www.car-videos.com/performance/

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Documents

1 Unit: Graphing Motion Objectives: Describe types of straight line motion. Design experiments to collect data and analyze motion. Use graphs to describe