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=Chapter 2=

Notes 9/7 Constant Speed
 

Lab: A Crash Course in Velocity (Part 1)
(Part 1) Honors Physics

**Objective:** What is the speed of a Constant Motion Vehicle (CMV)?

**Available Materials**: Constant Motion Vehicle, Tape measure and/or metersticks, spark timer and spark tape

**Hypothesis:** Yellow car will move less than 1 cm/s. A distance can be measured between two set points. A position-time graph tells you the position of a certain object at a certain time.

**Data**: Position- Time Data for CMV 

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Analysis:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The CMV was moving at a constant speed and the graph portrays that because it is linear. The slope is the average velocity. My hypothesis was accurate because the yellow CMV was going slow and was not traveling faster than 1 cm/s.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Discussion questions:**
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Why is the slope of the position-time graph equivalent to average velocity?
 * 2) The slope is the change in y over the change in x. In our graph the x axis represents time while the y axis represents change in position. The change of position over the change in time is equation for average velocity.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Why is it average velocity and not instantaneous velocity? What assumptions are we making?
 * 4) Instantaneous velocity is for an object that has a range of speeds but we are assuming that the CMV is going at a constant speed therefore we would use the average velocity.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Why was it okay to set the y-intercept equal to zero?
 * 6) When it was zero time, the position of the CMV did not move therefore it was automatically zero.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What is the meaning of the R2 value?
 * 8) R is a statistical term that displays the value of the prediction for future outcomes that are likely from the model.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">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?
 * 10) It would start out in the same place because at zero time, the CMV has not moved and from then on the points will be below the first graphs at the same time intervals. It would have a smaller slope and velocity because each position would be smaller.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Conclusion**: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">With our CMV, the results we got were not completely accurate with my hypothesis. The slow yellow CMV with one battery was moving a little more than 1 cm/s which was close to my hypothesis of moving a little less than 1 cm/s. My slope and velocity was 17.633. There could have been a few sources of error in this lab; someone moving the ruler, the dots not being precisely the same distance apart, as well as the issue of point of view when reading the thick meter stick. The way to get rid of these errors is to use a flat source of measurement like a tape measure or ruler which will be stuck to the desk perfectly parallel with the spark tape.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Kinematics HW 9/8 Lesson 1
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">1.What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> We discussed speed, which refers to the rate an object moves in a certain amount of time. Velocity refers to the rate at which an object changes its position.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">2.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. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The reading explained displacement too which confused me a little in class but after rereading the sections I understand it is the moving of something from its place or position.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">3.What (specifically) did you read that you still don’t understand? Please word these in the form of a question. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> I understand everything!

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">4.What (specifically) did you read that was not gone over during class today? <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Scalars and vectors were something I read about in the reading but we never talked about in class.

Notes On HW: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> mechanics = the study of the motion of objects <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Kinematics = the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Scalars = quantities that are fully described by a **distance** (or numerical value) alone <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Vectors = quantities that are fully __described by both a distance and a direction__ <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Distance = a scalar quantity that refers to the distance the object has **covered during its motion** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Displacement = a vector quantity that refers to "how far out of place an object is"; it is the object's **overall change in position** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Speed = a scalar quantity that refers to the speed the object is moving <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Velocity = a vector quantity that refers to the **rate at which an object changes its position** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Instantaneous Speed = the speed at any given __instant__ in time <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Average Speed = the average of all instantaneous speeds; found simply by a distance/time ratio <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Notes 9/9 Motion and Ticker Tape Diagrams

 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">kinematics= study of motion signs are made up
 * V= change in distance/ change in time
 * distance traveled/ time of travel
 * Average speed= distance time ratio of a trip
 * Constant speed= not changing
 * Instantaneous speed= a certain speed at a certain position
 * Four types of motions
 * At rest
 * Constant speed
 * Not changing
 * Increasing speed
 * Decreasing speed
 * BOTH ACCELRATION
 * Changing speed
 * Motion diagrams
 * V= 0
 * A= 0
 * à àà
 * a=0
 * arrows= velocity
 * arrows are the same length therefore are the same velocity
 * à -- à - à
 * getting faster so the acceleration is positive
 * à a
 * à -- à à
 * getting slower
 * ß a
 * the direction of the arrows matters
 * ß ßß
 * a=0
 * can go down
 * rotate the arrows so that it fits the object at hand
 * ticker tape diagrams
 * [[image:Screen_shot_2011-09-09_at_9.45.27_AM.png]]
 * signs are made up
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">which ever way the arrow points is the sign
 * refer to the graph in the direction things are positive and negative

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Motion with Diagrams HW 9/11 Lesson 2

 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I already understood the ticker tapes from the lab and how the position of the dots will distinguish if the object the ticker tape is attached to is fast or slow. The distance between the dots defines the object's position change during the time interval. The slower the object the closer the dots are to one another while the faster objects have more space between them. Vector diagrams depict the direction of the motion as well as the speed. The vector's symbol is an arrow and points into the specific direction the object was moving. The magnitude or length of the arrow changes due to speed increasing.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">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.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I was a little confused on what the distance between the dots on ticker tape meant but now I know that the length the dots are apart indicates the position change of the object in that specific time interval.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I understand everything very well after reading.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What (specifically) did you read that was not gone over during class today?
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Everything was discussed in class!

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Notes 9/12 Graphical Representations of Equilibrium
>>>
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">How can you tell that there is no motion on a…
 * position vs. time graph
 * It is a horizontal line that lies at a certain position the entire time
 * velocity vs. time graph
 * It is a horizontal line that lies on zero the entire time
 * acceleration vs. time graph
 * It is a horizontal line that lies on zero the entire time
 * [[image:rest.png width="480" height="291"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">How can you tell that your motion is steady on a…
 * position vs. time graph
 * When the points for position at a certain time create a linear graph.
 * velocity vs. time graph
 * There should be a constant velocity because the speed and direction is constant.
 * acceleration vs. time graph
 * There should be no acceleration because the motions are at a constant speed.
 * [[image:constant.png width="640" height="211"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">How can you tell that your motion is fast vs. slow on a…
 * position vs. time graph
 * Slow motions gradually ascend to higher position while faster motions achieve positions quicker.
 * velocity vs. time graph
 * The velocity for a slow motion line pretty much hugs the zero line not really moving far away from it while the faster motion has a higher velocity therefore is not as close to the line as the slow motion.
 * acceleration vs. time graph
 * The acceleration is constant for both graphs so they are both hugging the zero line.
 * [[image:slow.png width="720" height="259"]]
 * FAST
 * [[image:fast.png width="720" height="256"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">How can you tell that you changed direction on a…
 * position vs. time graph
 * The line starts out by going up in a linear line but than has a huge peak. The line descends from there because the direction changed.
 * velocity vs. time graph
 * There is a huge change in the graph and the velocity gets really big and really small in the middle of the graph.
 * acceleration vs. time graph
 * There is a huge change in the graph and the acceleration gets really big and really small in the middle of the graph.
 * [[image:change_position.png width="557" height="340"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What are the advantages of representing motion using a…
 * position vs. time graph
 * It shows you the position every second and the change in distance the motion detector picked up when the person moved.
 * velocity vs. time graph
 * You see the speed with every step and the direction is determined on the graph because it goes into the negatives.
 * acceleration vs. time graph
 * You are able to determine if the person is gaining speed when walking
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What are the disadvantages of representing motion using a…
 * For all of the graphs there is the disadvantage that humans pause in between steps to distribute their weight which makes the graph oscillate.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Define the following:
 * No motion= at rest
 * Constant speed= consistently moving at the same rate with every step the person takes

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Notes 9/13
>
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Position= where are you located
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Covering the same distance in the same amount of time
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Smaller or lower line is slower because it has a lesser slope
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Faster motion line has a steeper slope
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Slope=velocity
 * __<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Negative slope= going back to where you started or the back to the origin __
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Away from origin= positive**
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Negative velocities don’t mean you are going slow
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">at rest constant speed
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">[[image:Photo_on_2011-09-19_at_18.03_#2.jpg width="512" height="384"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">[[image:Photo_on_2011-09-19_at_18.03_#3.jpg width="448" height="336"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">THE BIG 5 IS ABOVE
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">[[image:Photo_on_2011-09-19_at_18.04.jpg width="512" height="384"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">[[image:Screen_shot_2011-09-20_at_8.21.16_PM.png]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">[[image:Screen_shot_2011-09-20_at_8.20.39_PM.png]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">[[image:Screen_shot_2011-09-20_at_8.20.24_PM.png]]

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Acceleration HW 9/13
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">1.What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">2.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. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">3.What (specifically) did you read that you still don’t understand? Please word these in the form of a question. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">4. What (specifically) did you read that was not gone over during class today? <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The Rule of Thumb > depending on the slope as well as the increase or decrease of speed will help determine the acceleration > If an object is slowing down, then its acceleration is in the opposite direction of its motion > When an object is speeding up, the acceleration is in the same direction as the velocity 
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Acceleration is the change of speed of a moving object. An object must be changing velocity to be changing acceleration. A constant acceleration is when an object is changing the same amount of velocity in the same time interval.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Rule of Thumb: positive accerlation is when the direction is going up or to the right while negative acceleration means down or to the left
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I was a little confused on what it meant when you said in class about an object with a constant velocity is not the same a constant acceleration. An object with a constant velocity is not accelerating and an object that’s velocity is constantly changing or varying amount is an accelerating object.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I think I understand everything very well but I would just like to clear up the reasons why the rule of thumb works?

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Notes 9/14
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Lab 9/14 Acceleration Graphs on an Incline
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The Effects of Acceleration on Position- Time Graphs <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Septemeber 14, 2011 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Lab Partner: Jenna Malley <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Objectives:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Procedure**:
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What does a position-time graph for increasing speeds look like?
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What information can be found from the graph?
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Set up the ramp on one textbook
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Put the ticker tape through the spark timer and tape the ticker tape on the dynamics cart
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Put the dyamics cart on the track
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Turn the spark timer on and let go of the dynamic cart
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Take the tape off the cart and measure the distance between dots
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Record the time and positions on excel and create the graph

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Available Materials:**
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Spark tape, spark timer, track, dynamics cart, ruler/meterstick/measuring tape

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Hypothesis:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The position time graph will be a positive graph that has a slow that will become steeper like a J curve. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">From this graph we will be able to find the position of the object at any recorded time and its increasing velocity.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Data**: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Analysis:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">a) Interpret the equation of the line (slope, y-intercept) and the R2 value. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">b) Find the instantaneous speed at halfway point and at 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.) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**half= 23.01 cm/s** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**end= 16.4 cm/s**
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The equation of y= Ax2 + Bx is known to be the equation of the change in distance= initial velocity (time) + ½ acceleration (time)2. So A is ½ the accleration while B is initial velocity. X is time while y is the change in distance.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">R2 is .99982 which is very close to one which shows how accurate our graph is.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">We used polynomial trend lines rather than linear because the polynomial gave a better accuracy.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">c) Find the average speed for the entire trip.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">[[image:Screen_shot_2011-09-14_at_9.30.41_AM.png width="668" height="123"]]

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Discussion Questions:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Conclusion**:
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What would your graph look like if the incline had been steeper?
 * 2) The graph would be steeper therefore the position values would be a large quantity and there would be a greater change in distance.
 * 3) [[image:Photo_on_2011-09-14_at_17.11.jpg width="320" height="240"]]
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What would your graph look like if the cart had been decreasing up the incline?
 * 5) The graph would be increasing and then start to flatten out which means the accerlations is dying out.
 * 6) [[image:Photo_on_2011-09-14_at_17.11_#2.jpg width="384" height="288"]]
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Compare the instantaneous speed at the halfway point with the average speed of the entire trip.
 * 8) The instantenous speed of the graph was 23.01 cm/s while the average speed was 19.56 cm/s. They are close to each other but are not equal. The reasoning for this is the instantaneous speed is one speed in a range so it is logical if it is a little bigger than the average speed because it is an average of different speeds the cart traveled at.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?
 * 10) This makes sense because instantaneous speed is the speed for tone point. Because the tangent line only runs through one point on the graph and the axis' are position and time, the speed will be from the point.
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
 * 12) [[image:Screen_shot_2011-09-14_at_5.53.31_PM.png width="561" height="300"]]

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">This lab allowed us to see how acceleration and deceleration is represented in a position- time graph. The average speed of the cart was 19. 56 as the cart traveled for 2.00 seconds as it accelerated. The graph was steep and a J curve which made my hypothesis accurate because the speed slowly accelerated down the ramp. The graph had a positive direction. The source of error that could have occurred was measuring the distance between the dots on ticker tape because of the view looking at it. Next time, I would make my measurements more accurate by drawing lines from the dots to the rulers as well as having more trials to compare our results too.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">HW 9/15 Lessons 3 and Lesson 4
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">1.What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">2.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. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">3.What (specifically) did you read that you still don’t understand? Please word these in the form of a question. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">4. What (specifically) did you read that was not gone over during class today? <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">We learned everything!
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I understood hot find the slope for the different graphs and I already understood how to read the position time graph as well as the velocity time graph. The velocity time graph is made up of horizontal lines that change their velocity depending on the acceleration for certain time periods. The position time graph explain the positions of the object at certain times.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Acceleration=slope=velocity
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Finding the difference between the positive acceleration graphs and negative acceleration graphs is a little confusing but the pictures are helping me understand it a little better..
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I think I understand everything very well but I would just like to clear up the reasons why the rule of thumb works?

Notes on HW: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> position vs. time graphs = to describe motion <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">velocity= slope <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">negative acceleration= moving in the negative direction and speeding up <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> smaller slope to bigger slope positive acceleration=object is moving in the negative direction and slowing down

large slope to smaller slope/fast to slow negative velocity

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">positive velocity results in a line of zero slope <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">car is moving in the positive direction and speeding up= a //positive// acceleration <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">acceleration is negative, then the slope is negative (i.e., a downward sloping line) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">velocity would be positive whenever the line lies in the positive region <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">slope of the line was equal to the acceleration <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> the acceleration is positive, then the line is an upward sloping line - having a positive slope <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> the acceleration is negative, then the velocity-time graph is a downward sloping line - having a negative slope. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">the area bound by the line and the axes represents the displacement

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Notes 9/16
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Graphing Packet:
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">A <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">D <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">E <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">F <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">G

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Lab: A Crash Course in Velocity (Part 2)
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">9/21/2011 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Lab Partners: Jenna Malley, Sarah Malley, and Ryan Hall

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Procedure**: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">media type="file" key="Movie on 2011-09-21 at 08.57.mov" width="300" height="300" <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">media type="file" key="Movie on 2011-09-21 at 09.06.mov" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Calculations**: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Data**: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Points for Crashing CMV <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">yellow CMV blue CMV <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Crashing CMVS Catching Up CMV <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Analysis**: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I used the average of the positions for the experimental value in the percent error and percent difference formulas for the catching up CMV as well as the crashing CMV. The position values we received during the trials were all so close to each other that it was the wiser choice to average them together. The percent error as well as the percent difference was very low all under 3%.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Discussion Questions:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Conclusion: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Our calculations for the crashing CMV and the catching up CMV the time and distance we recorded was very close to the theoretical solutions. We received that the distance the yellow would travel for the crashing aspect would be 164.52 and all of the results we received were within couple of units digits difference. The same results occurred for the catching up aspect. There could have been a couple of sources of error for our lab but not to many because our percent error for each was very low. The catching up percent error was 1.42% while the crashing lab error was 2.5%. The source of error could have been our reaction to when the crash or catch up happened was delayed and therefore our measurements may be a little delayed. Also our blue car would veer off from the measuring tape during the crashing lab, this made the judgement call of position to be more based on the human eye than seeing them actually crash and knowing the exact spot they hit each other. I would change the lab by making our blue car go straight next to measuring tape this way it would not be as much of a judgement call that is delayed due to human response.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Where would the cars meet if their speeds were exactly equal?Sketch position-time graphs to represent the catching up and crashing situations. Show the point where they are at the same place at the same time.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">The cars would meet in the exact middle of the distance because they are both traveling at the same constant speed.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">﻿[[image:Screen_shot_2011-09-21_at_5.35.04_PM.png width="683" height="354"]]
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">They meet at 9.35 seconds at 160 cm.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; line-height: 0px;">[[image:Screen_shot_2011-09-21_at_5.59.26_PM.png]]
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The x axis= time(s)
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The y axis= position(cm)
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">This is the graph for the catching up and the blue CMV catches up to our yellow CMV at 3.2 s at 160 cm which is the point of intersection between the two lines.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Sketch velocity-time graphs to represent the catching up situation. Is there any way to find the points when they are at the same place at the same time?
 * 10) [[image:Photo_on_2011-09-21_at_18.59_#4.jpg]]
 * 11) velocity for blue CMV= 46.7 cm/s
 * 12) velocity for the yellow CMV= 17.33 cm/s
 * 13) No because a velocity time graph doesn't show the position of where the CMV at a certain time it shows the speed and direction of the CMV.
 * 1) No because a velocity time graph doesn't show the position of where the CMV at a certain time it shows the speed and direction of the CMV.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Egg Drop Lab 9/28
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Partner: Ali Cantor <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Final Prototype: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Description: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Our project is a cone made out of newspaper. It has four straws covered in newspaper used a wings in the middle of the cone. We crumpled a piece of paper and attached that with sewing string to the newspaper as a parachute. Inside, there was crumpled paper pushed towards the bottom and we put crumpled paper on top of the egg. The egg was closer to the bottom but had a paper cushion at the tip of the cone so it did not receive the impact of the fall.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Discussion/ Analysis: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">At first for our projection, we made a square basket made out of straws with the crumpled paper as the parachute. There was no top so we made an X shape with rubber bands and paper clips but they egg would fly out from the top. Then, we decided to use a cone shape with four wings and a parachute. We wanted to slow down the motion of the objection to protect the egg. Our egg only slightly cracked so it was in between a bleeding crack and a dry crack. The reason the crack was so small was because of the cone shape. When the cone goes straight down the tip crumples which softens the landing for the egg plus the papers we placed at the tip lessened the impact for the egg.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What would be fixed? <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The one problem with our project was that it would always land on its side. For next time, I think I would have made two big wings and a bigger parachute to make it land on the tip of the cone.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Calculations for Accelerations:

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Our prototypes acceleration was 7.26 m/s^2.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Free Fall HW 10/3
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">A free falling object is an object that is falling under only the influence of gravity. There are two important motion characteristics that are true of free-falling objects: they do not encounter air resistance and they (on Earth) accelerate downwards at a rate of 9.8 m/s/s known as the acceleration of gravity. An object that travels downward and speeds up, then its acceleration is downward.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">A curved line on a position versus time graph signifies an accelerated motion. The small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (downward) velocity.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">This graph reveals that the object starts with a zero velocity and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The velocity of a free-falling object is changing by 9.8 m/s every second. vf = a * t <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. d = 0.5 * a * t2 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Free-fall is the motion of objects that move under the sole influence of gravity; free-falling objects do not encounter air resistance. . All objects free fall at the same rate of acceleration, regardless of their mass.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Free Fall Lab 10/5
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Objective**: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What is the acceleration of a falling body? <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Hypothesis:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The weight would increase its acceleration as it is dropped from the balcony. The velocity would increase negatively. So it would be a neggative graph that was going to be in the fourth quadrant. The slope will be the acceleration or g.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Data: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">﻿Position TIme Graph <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Velocity Time Graph <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Analysis: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">These pictures explain the equations and how they were derived. The slope intercept form equation is the same as the velocity formula. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Percent Error and Difference <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The shape of the position time graph is a curve that is increasing positively. The velocity time graph was increasing in a positive acceleration. Both of these graphs are positive because we recorded them positively but because the object is falling it should be negative. We found our slope or acceleration from the y intercept form of the velocity graph's trend line. The slope was 659.39cm/s^2 which was the lowest out of the classes which was the furthest acceleration for free fall 981 cm/s^2. The y intercept form is derived from the formula Vf= at + Vi therefore acceleration= slope. he The equation y=1/2at^2 +Vi t is derived from the standard form equation of Ax^2 +By=y therefore a=2A which is the acceleration while the B is the initial velocity. The R^2 is .999 which means that it was very accurate.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">DIscussion: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> The shape of an increasing linear line is correct but I thought that it would be negative due to the fact that free falll has a negative acceleration of 981 cm/s <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> The curve looks the way it should but with the I also thought that the graph would be a negative increase. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> We have the lowest results in the class. The percent difference I received from the calculations was 21.45% which is va larger than normally. The average for the class was 839.417 cm/s^2 while our acceleration was 659.39 cm/s^2 which was very far from the theoretical acceleration of 981cm/s^2. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> The object's acceleration increased every second but the amount it increased was not uniform. The accleration increased between every second because when you subtracted the final position by the initial position at that point it was not a uniform number it was a growing number each time. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The two main factors that would cause acceleration due to gravity be either higher or lower than 981 cm/s^2 would be friction and air resistance. Friction is the moving of one object against another and air resistance is the forces that oppose that the relative motion of an object. It creates n error with gravity.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Does the shape of your v-t graph agree with the expected graph? Why or why not?
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Does the shape of your x-t graph agree with the expected graph? Why or why not?
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Did the object accelerate uniformly? How do you know?
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Conclusion: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">My hypothesis was correct in the sense that acceleration would increase as the object fell further down and technically it was negative because it was falling but our graphs do not display. The graphs portray the increase of position and velocity of this object. Our results gave us an acceleration which was 659.39 cm/s^2 which was very low and not very close to the theoretical slope or acceleration of 981 cm/s^2. This was the reason our percent error was kind of large it was 32.8 %. I think a large reason to why our acceleration was so off was because the measuring tape and ticker tape moved creating an error. Another reason was due to the friction that the ticker tape was dragged through the ticker tape timer because it was being held at a weird angle. Next time I would try and hold the ticker tape timer more vertical and hold the long tape in my hands to make sure it went through perfectly.

Notes 10/7 Free Fall Problems