Ch2_WangS

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 * Chapter 2 **

**Class notes: Constant Speed**__Position__: where an object is located in reference to its surroundings __Distance__: how far an object has traveled, regardless of direction __Displacement__: how far an object is from its starting location; must have a reference point and include a direction __Velocity__: rate of change of position (how fast an object is going). This can be negative. Speed is the same thing, but can't be negative. Velocity must reference direction. (Measures displacement, not distance) __Vectors__: size and direction __Scalar:__ size only



**Lesson 1: Describing Motion With Words** B,C,D


 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * Since these readings are about topics that have been covered in class, I was familiar with most of them. Two topics that I was already familiar with (from class) were the definitions of distance and displacement. Displacement refers to an object's overall change in position, and distance refers to how much an object has traveled overall. The example used with the physics teacher only reaffirmed my knowledge.
 * 1) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
 * A concept I had trouble with during class was the definition of scalar vs. the definition of vector. I did not understand if a quantity could be both a scalar and a vector, instead of just one or the other. For example, are all scalars also vectors, but not all vectors are scalars? (This is sort of like the statement "All squares are rectangles, but not all rectangles are squares") The reading helped me see that it is not possible for a quantity to be both a scalar and a vector. It can only be one.
 * 1) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * I do not have any questions, as the questions I had from class were answered in the readings.
 * 1) What (specifically) did you read that was not gone over during class today?
 * Instantaneous speed was not covered in class today. It is "the speed in any given instant in time". It is compared to the speed on the speedometer of a car. It is different from average speed because objects do not travel at consistent speeds all the time.

E


 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * I already knew from our discussion in class that the formula for acceleration is (final velocity - initial velocity) / time. This is a different formula from velocity. In class, we also talked about constant acceleration. This is when an object moves faster or slower at a consistent pace. This is unlike constant speed because the object is either getting faster or slower. The object stays in motion, but does not move at the same rate for a set distance. Instead, the velocity either increases or decreases by a constant amount each second.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
 * I did not have any questions from class that the reading helped to clarify.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * I do not have any questions, as the questions.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that was not gone over during class today?
 * We didn't go over the free-falling object in class. A free falling object is the acceleration of an object when it is dropped from above ground. A free falling object does not have constant acceleration. Instead, it goes faster and faster, so its acceleration increases as it falls.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">**Speed of a Constant Motion Vehicle Lab: September 9** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">**Partner:** Nicole Tomasofsky

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">**Purpose:**The purpose of this lab is to find the speed of a CMV, a constant motion vehicle, and see what information can be gleaned from position time graphs. Also, from this lab, I am trying to find how precisely you can measure distances with a meter stick.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Objectives:**


 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How precisely can you measure distances with a meter stick?
 * 2) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How fast does the CMV move?
 * 3) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What information can you get from a position time graph?

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Materials:**


 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">spark timer
 * 2) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">spark tape
 * 3) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">meter stick
 * 4) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">masking tape
 * 5) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">CMV

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Hypothesis:**


 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How precisely can you measure distances with a meter stick? You can measure distances to the nearest millimeter using the meter stick. This is my hypothesis because I have used meter sticks in the past and know that there are millimeter marks on the meter stick, and they are the smallest unit of measurement.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How fast does the CMV move? 75 cm/s. This is my hypothesis because
 * 3) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What information you get from a position time graph? You can get the instantaneous speed and average velocity of an object.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Data:**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Length of laptop = 30.0 cm

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Average velocity/speed of CMV:

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Average speed = 45.12 cm / 1 second

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">= 45.12 cm/s

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">The CMV moves 45.12 cm/s

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Discussion questions**


 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Why is the slope of the position-time graph equivalent to average velocity?
 * Slope is nothing more than rise over run, or y/x. The formula for average velocity is displacement over time elapsed. In my graph, position is the y axis, and time is the x axis. So in this case, y/x = displacement/time. This makes the slope equal the average velocity of the CMV.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Why is it average velocity and not instantaneous velocity? What assumptions are we making?
 * Average velocity is more accurate than instantaneous velocity because instead of just looking at one point on the graph, all our data is taken into consideration. The slope determines the average velocity, and individual plots represent the instantaneous velocity. Since we are using the slope of the line to find velocity, and not individual plots on the graph, we are finding the average velocity. We are making the assumption that the CMV is going at a constant speed.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Why was it okay to set the y-intercept equal to zero?What is the meaning of the R2 value?
 * It is okay to set the y intercept equal to zero in this situation because the y axis measures position, and as our CMVs do not travel backwards, it is impossible for them to have a negative position. The CMVs start at a position of (0,0) because the time and position are both zero.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What is the meaning of the R2 value?
 * The R2 value tells you how accurate your graph is. It does this by setting a trendline through all the points in the graph. Then, the R2 value tells you how close the trendline is to the points you plotted in your scatter gram. The closer to 1.0 it is, the more accurate your results.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">If you were to add the graph of another CMV that moved more slowly on the same axes as your current graph, how would you expect it to lie relative to yours?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">I would expect the graph to have a smaller slope. This means that my original graph would have a steeper slope than the 2nd, new, graph.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Conclusion:**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> For this lab, there were three objectives: How precisely can you measure distances with a meter stick? How fast does a CMV move? What information can you get from a position time graph? My hypothesis for the first question was that you could measure up to the nearest millimeter. It turns out that you can guess the distance between two millimeter marks, so you can get an even more precise measurement than I had predicted. I had also hypothesized that a CMV could travel 75 cm/s. But, my data shows that the speed of the CMV was actually 44.12 cm/s. Therefore, my hypothesis was wrong. I had also hypothesized that you could get two pieces of information from a position time graph: instantaneous velocity and average velocity. The data my partner and I collected supports this hypothesis.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> There are many sources of error that could have contributed to inaccuracies. For example, the meter stick could have moved while my partner and I measured the distance between the dots. This problem could have been remedied by taping down the meter stick. Also, it was hard to get an accurate reading of the distances because the meter stick is made of wood, and the centimeter and millimeter marks do not sit directly on the page, next to the dots that my partner and I were measuring. Instead, they sit a couple of centimeters up, so depending on what angle you choose to read the measurement at, you could have different distances. Using a tape measure could have eliminated this source of error. It is important to learn how to take the proper measurements of a distance because in real life, a couple of centimeters could make a huge difference. For example, if an architect designs a building, but accidentally makes the door frames a couple of cm too small, then the doors can't fit. This would be a huge problem.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Overall, I feel that this lab was a success, and my partner and I made the best of the materials that were available to get the most accurate data.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Class Notes: Graph Shapes (At Rest and Constant Speed)
//
 * Position-time graphs**

//**velocity-time graphs**//

//

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">**Lesson 2: Describing Motion With Diagrams** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">A,B,C


 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * There were two things that I read about that I already understood from our class discussion. They are:
 * Ticker tape diagrams
 * Ticker tape diagrams are used to describe motion. A long tape is threaded in a specialized machine, and dots are created on the tape. A dot is created X times a second, so the further apart the dots, the faster the tape is going. The closer the dots, the slower it is going. If the dots get more crowded on the paper towards the end, it is showing acceleration. However, this device only measures scalar quantities, as direction of movement is not recorded.
 * Vector Diagrams
 * Vector diagrams are diagrams with arrows and labels. There are two kinds of arrows. Ones that are labeled with "a" show acceleration (whether is is positive or negative) and arrows that are marked with "v" show velocity. If the object moving has positive velocity, the arrows get larger. Negative velocity means the arrows get smaller. If an object is traveling at a steady rate, the arrows are the same size.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
 * I did not have any questions from class that the reading helped to clarify.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * I do not have any questions.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that was not gone over during class today?
 * We went over everything in the reading in class.

Class Notes: The Big Five (Equations)
These equations are the main ones used when dealing with motion in physics.

Note: t means change in time, or delta t

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Lesson 3: Describing Motion with Position vs. Time Graphs**

 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * I already knew from our classroom discussion that if two position time graphs of constant velocity were to be compared, the one that depicts the faster velocity would have the larger slope and the steeper graph.
 * Before reading this, I also knew that slope is equal to rise over run.This is a concept that I have explored both in math and in physics.The formula for slope, m= (Y1-Y2 / X1-X2) is something that I was familiar with before I read this lesson.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
 * A concept I had trouble with during class was whether position time graphs had a negative y axis.I was confused because velocity-time graphs could have negative y-values.This reading helped me see that it is impossible for an object to have a negative position.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * I do not have any questions, as the questions I had from class were answered in the readings.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that was not gone over during class today?
 * I believe everything in the reading was covered in class.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Lesson 4: Describing Motion with Velocity vs. Time Graphs**

 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * I already knew from our classroom discussion that if the velocity-time graph was a straight horizontal line with a slope of 0, then the object that was represented would be either moving at a constant speed or at rest.
 * From class, I learned that the area of the region between the line of and the axes in a velocity time graph show the displacement.The information in the reading only reaffirmed my knowledge.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
 * I did not have any questions that the reading helped to clarify.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * One question I have is: What if there is a negative velocity?Would displacement still be shown by the area of the region bounded by the line and axes?
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What (specifically) did you read that was not gone over during class today?
 * I believe everything in the reading was covered in class.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">At rest: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Slow away from sensor:

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Fast away from the sensor: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Slow towards the sensor: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Slow away and fast away together for comparison: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How can you tell that there is no motion on a…
 * 2) position vs. time graph: The graph is a horizontal line
 * 3) velocity vs. time graph: The graph is a horizontal line at y= 0
 * 4) acceleration vs. time graph: The graph is a horizontal line at y=0


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How can you tell that your motion is steady on a…
 * 2) position vs. time graph: The graph is a straight line, and is linear. It is going diagonally.
 * 3) velocity vs. time graph: The graph is a straight horizontal line above the x axis
 * 4) acceleration vs. time graph: The graph is a straight horizontal line on the x axis at y=0


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How can you tell that your motion is fast vs. slow on a…
 * 2) position vs. time graph: If the motion is fast, the graph will have a steeper slope, and if the motion is slow, the graph will have a more horizontal slope that is not as steep.
 * 3) velocity vs. time graph: You can't tell
 * 4) acceleration vs. time graph: You can't tell


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How can you tell that you changed direction on a…
 * 2) position vs. time graph: The slope will be positive for the first half of the graph, but be negative for the second half. For example, if the slope is 5 on the first half of the graph, it will be -5 on the second half. (or vice versa)
 * 3) velocity vs. time graph: You can't tell
 * 4) acceleration vs. time graph: You can't tell


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What are the advantages of representing motion using a…
 * 2) position vs. time graph: You can see changes in direction and where the person/ object was at any point in time
 * 3) velocity vs. time graph: This graph shows instantaneous speed well.
 * 4) acceleration vs. time graph: You can see changes in speed with this graph


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What are the disadvantages of representing motion using a…
 * 2) position vs. time graph: You can't see the changes in speed as well
 * 3) velocity vs. time graph: If the velocity doesn't change (aka if the object/ person is going at constant speed), this graph doesn't show anything . It also doesn't show position or direction.
 * 4) acceleration vs. time graph: If the velocity doesn't change (aka if the object/ person is going at constant speed), this graph doesn't show anything . It also doesn't show position or direction.


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Define the following:
 * 2) No motion: Nothing is moving. The graph is unchanging with velocity and acceleration at zero.
 * 3) Constant speed: The position is changing, but velocity and acceleration are at zero.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Cart and Ramp Class Activity
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Position time graphs and Velocity- time graphs

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Decreasing Acceleration/ Up the ramp towards the sensor <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Increasing Acceleration/ Down the ramp away from the sensor <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Position time graph practice 9/15
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">


 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Describe the motion of the car (qualitatively) during each segment.
 * AB at rest
 * BC constant towards
 * CD at rest
 * DE constant away
 * EF at rest
 * FG constant towards
 * GH constant away
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Describe the change in position of the car during each segment.
 * AB none
 * BC 10 to 0 (-10)
 * CD none
 * DE 0 to -16 (-16)
 * EF none
 * FG -16 to 0 (16)
 * GH 0 to 14 (14)
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Calculate the velocity of the car during each segment.
 * Distance / time
 * AB
 * BC -10/2 = -5 m/s
 * CD
 * DE -16/ .5 =-32 m/s
 * EF
 * FG 16/1 = 16 m/s
 * GH 14/2 = 7 m/s
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What is its //average speed// for the entire 12-s?
 * Total distance/ Total time (add displacements without signs)
 * 56 m/11 s = 5.1 m/s
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What is its //average velocity// for the entire 12-s?
 * Displacement/ time
 * Final position – initial position = displacement
 * 4/11 = .44 m/s
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What is the acceleration of the car during each segment?
 * 0 for each segment because they are constant speeds

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Acceleration Graphs Lab: September 16
<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">Partner: Nicole Tomasofsky

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">**Objectives:** What does a position time graph for increasing speed look like? What information can be found from the graph? <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">**Hypothesis:** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">**Available Materials:** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 110%; text-align: left;">Spark tape, spark timer, track, dynamics cart, ruler/meterstick/measuring tape <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Procedure:**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What does a position-time graph for increasing speeds look like? It is a curved line, with a positive slope. The slope is getting steeper.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What information can be found from the graph? You can find the average speed and instantaneous speed.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Gather materials. This includes: Spark tape, spark timer, track, dynamics cart, ruler/meterstick/measuring tape.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Set up the ramp by placing the end of the track on a textbook.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Set up the spark timer by plugging it in and placing it at the top of the track.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Run a piece of spark tape through the spark timer and tape it to the cart.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Set the spark timer to 10 Hz
 * 6) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Set the cart at the top of the track and let it roll down the ramp.
 * 7) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Save this piece of spark tape.
 * 8) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Now, set the cart at the bottom with the timer.
 * 9) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Push the cart up, so the tape runs through the timer.
 * 10) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Save the tape and make sure there are at least 10 spark marks on each piece of tape.
 * 11) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Using a meter stick, measure the distance between the dots on both pieces of tape.
 * 12) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Record this data in an excel spreadsheet and analyze.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Data:**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Table:**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Graph:** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Analysis:** >> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Decreasing speed: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Graph with tangent lines drawn in: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Interpret the equation of the line (slope, y-intercept) and the R2 value.**
 * 2) Interpretation: Linear trend lines are used with linear graphs. Since our graph is not linear (y=mx + b), but polynomial (y=ax^2+bx+c)a polynomial line of best fit is the best option. This line of best fit tell us many things. First, the R^2 value tells us how close to being perfect our graph is (1.0 is perfect). The y-value tells us the location of the cart at any time. Also, the 2a (2 times the a value) gives us the average acceleration. Also, the b value shows the initial velocity.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">Increasing speed:
 * Linear Line= y = 33.167 x - 6.9016/ r^2 = .97068
 * Polynomial Line= y= 10.663x^2 + 11.842x - .1485/ r^2= .99991
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Decreasing speed:
 * Linear Line = y =42.219x + 43131 / r^2 = .96279
 * Polynomial Line= y = -24.762x^2 + 72.133x - 1.1345/ r^2= .99888
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Find the instantaneous speed at halfway point and the end. (You may find this easier to do on a printed copy of the graph. Just remember to take a snapshot of it and upload to wiki when you are done.)**
 * 2) Increasing speed:Graph with tangent lines drawn in:
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">[[image:Screen_shot_2011-09-19_at_9.10.12_PM.png width="800" height="494"]]
 * Halfway point = 1.0 s
 * 2 points on line: (.3,0) (.5,5)
 * slope = 25
 * instantaneous speed = 25 cm/s
 * End = 2.0 s
 * 2 points on line: (1.5, 33) (2, 63)
 * slope = 60
 * instantaneous speed = 60 cm/s


 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Halfway point = 0.60 s
 * 2 points on line: (0,6) (0.5, 28)
 * slope = 44
 * instantaneous speed = 44 cm/s
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">End = 1.20 s
 * 2 points on line: (0,31) (.3,36)
 * slope = 50/3
 * instantaneous speed = 50/3 cm/s

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">c) Find the average speed for the entire trip. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Decreasing speed: distance traveled/ time elapsed = average speed <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">= 66.40cm/2.0s <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">=33.20 cm/s <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Increasing speed: distance traveled/ time elapsed = average speed <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">=49.98 cm/1.20 s <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">=41.65 cm/s

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">**Discussion Questions:**
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What would your graph look like if the incline had been steeper?
 * 2) The graph would have a larger slope and a steeper graph. The curve of the graph would be more predominant, since the acceleration would be greater.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">What would your graph look like if the cart had been decreasing up the incline?
 * 4) The initial curve would be steep and noticeable (since the cart is traveling faster in the beginning), but the line would flatten out. Also, the line would go away from the origin.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Compare the instantaneous speed at the halfway point with the average speed of the entire trip.
 * 6) Increasing speed graph:
 * 7) half way point has a velocity of 25 cm/s.
 * 8) average velocity is 33.20 cm/s.
 * 9) Average velocity is faster
 * 10) Decreasing speed graph:
 * 11) half way point has a velocity of 44 cm/s.
 * 12) average velocity is 41.65 cm/s.
 * 13) Halfway point velocity is faster.
 * 14) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
 * 15) You cannot find the slope (or change) one point--you need two points. A tangent line offers a slope, and since it touches only the point on the graph it is tangent to, it is representing the slope of the line. The slope of the one line shows the speed at that specific moment, which is instantaneous speed.

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<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Conclusion

For my hypothesis, I stated that you could find the instantaneous speed and average speed from a position time graph. From this lab, I learned that you can also find determine initial velocity, and average acceleration. I also hypothesized that the position time graph for increasing speed would look like a curved line with a slope that is getting steeper. The graph is also moving away from the origin. This hypothesis proved to be correct. There are multiple possible sources of error for this experiment. For example, since we had two strips of tape, maybe we got them mixed up. This could have been easily remedied by labeling the strips of tape. Also, another error that could have occurred was that our measures of the distance between the dots were inaccurate. Maybe the tape moved around while we were measuring. This could have been fixed by taping the stick to the meter stick.

Crash Lab Purpose: The purpose of this lab is to determine the distance two CMVs must travel in order to crash. Also, we are trying to see how far a slower CMV must travel before a faster CMV catches up to it. Procedure:

Part A: media type="file" key="Movie on 2011-09-23 at 11.31.mov" width="300" height="300"

Part B: media type="file" key="Movie on 2011-09-23 at 11.36

Data and Calculations: Speed of CMV 1 (blue): 44.159 cm/s Speed of CMV 2 (yellow): 12.897 cm/s Part A) Find another group with a different CMV speed. Find the position where both CMV’s will meet if they start //at least// 600 cm apart, move towards each other, and start simultaneously.







They will crash at 464.38 cm from the blue car and 135.62 cm from the yellow car if the two cars start at 600 cm apart. Part B) Find the position where the faster CMV will catch up with the slower CMV if they start // at least // 1 m apart, move in the same direction, and start simultaneously. The yellow CMV (slower) will travel 41.25 cm, and the blue CMV (faster) will travel 141.25 cm before the faster CMV catches up with the slower CMV. (This is assuming the blue CMV starts 1 meter, or 100 cm, behind the yellow CMV)