Ch2_CantorA

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**Kinematics** **Constant Speed**

=CMV Lab = ﻿Ali and Caroline 9/8 ** Objective: **What is the speed of a Constant Motion Vehicle (CMV)? ** Hypotheses ** : A CMV moves 20 ft/15 secs --> 609.6 cm/15 secs --> 40.64 cm/sec. Distances can be measured to the nearest millimeter, but then, an educated guess must be used for the next decimal place. A time position graph tells the time relative to the distance away from zero (which is also known as the position). This, hopefully, should be a linear function.

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

**Analysis** Essentially, the graph of the CMV shows that it is moving at a constant speed, because of the slope of the line (positive direction). At each interval, it is moving approximately the same distance away from the point before it. ** Discussion questions ** ** Conclusion ** My results showed that the average speed of a CMV was 37.962 cm/s. It seems that as the time sped up, the distance the CMV traveled lessened. My hypothesis was that the CMV would travel 40.64 cm/s. Although it did not travel as far as I had originally thought, the CMV still traveled in a 5 cm range to my guess. Therefore, I consider it fairly accurate. However, whenever performing an experiment, there is always room for error. This error could be found in the instruments that we used for measuring the length between the dots on the spark tape. The meter stick may have slid while we were recording down the measurements; the shape of the meter stick also was thick, so it made it difficult to make out the exact numbers. Another aspect of error was that the measurements weren’t as precise as they could have been. If we had more effective, digital tools, we could have gotten the exact measurement. <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">In order to minimize error, next time, we could use an instrument that does not slide and is flatter, therefore making the numbers easier to read. Something like measurement tape could be more effective. Rather, a digital tool could be used for better accuracy.
 * 1) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Why is the slope of the position-time graph equivalent to average velocity?
 * 2) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Slope is the measure of Δy/ Δx
 * 3) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">in this case, the Δy=Δd (distance) and the Δx= Δt (time)
 * 4) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">therefore; Δy/ Δx = Δd/ Δt = V
 * 5) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Why is it average velocity and not instantaneous velocity? What assumptions are we making?
 * 6) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Instantaneous velocity is at one point, so it only accounts for one point. Average velocity takes all of the points into account; therefore, it is more accurate. <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif;">We are assuming that all of the values will be relatively close, and not many outliers will exist.
 * 7) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Why was it okay to set the y-intercept equal to zero?
 * 8) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">It is okay to set the y-intercept equal to zero because since the y-axis is the position, if it’s at zero, it will not be moving. This was the starting point from which or average velocity was graphed
 * 9) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What is the meaning of the R2 value?
 * 10) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">R2 is the percentage of points described by the trend line. It is a tool to help us know how “fit” our data is compared to the trend line. If the value is around .99… the data is accurate.
 * 11) <span style="color: #000000; 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?
 * 12) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">If it were to be slower, the line would lie below our trend line. It is still traveling in the same amount of time, but the distance traveled won’t be nearly as much.

=<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 27px;">**CMV Lab Part 2** = <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Ali, Caroline, Dani, Julia 9/21

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Objectives ** : Both algebraically and graphically, solve the following 2 problems. Then set up each situation and run trials to confirm your calculations.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Available Materials ** : Constant Motion Vehicle, Tape measure and/or metersticks, Masking tape (about 30 cm/group), Stop watch, spark timer and spark tape


 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">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.



<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">According to our calculations, the blue car should travel 372.321 cm and then crash into the yellow car (which would have moved 229.214 cm). Below is a video of what ACTUALLY happened. The data table below it shows each trial and the distance each CMV actually moved. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="My First Project - Medium.m4v" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Here, the two cars crash at a certain point. We then proceeded to mark the place where they met, proving our calculations to be approximately correct.




 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">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.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">According to our calculations, the blue car should travel 260.156 cm and then become parallel with the yellow car. Below is a video of what ACTUALLY happened. The data table below shows each trial and the distance it took for the blue to catch up. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="new - Medium.m4v" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The faster of the two cars (blue) is catching up to the yellow car at a certain point. We then proceeded to mark the place where they met, proving our calculations to be approximately correct.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Analysis ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Based on this percent error of .57%, I can conclude that our results were very accurate for the case of the blue car striking the yellow car. The smaller percent that we have, the better our results are in actuality. We chose to take an average of or experimental values because all of our experimental values were very close to each other. For percent difference of the crash, we took the average experimental value and subtracted the individual value. Then, we divided it by the average value and multiplied by 100 to get a percentage. Our percentages were very small, thus demonstrating precision. Overall, between these two methods, we can conclude that our results were very accurate and precise.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Part A: crashing **

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; line-height: 0px; overflow: hidden;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; line-height: 0px; overflow: hidden;"> <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; text-align: left;">Once again, we used percent error again to find out how accurate the results for Part B were. As shown above, our results turned out to be extremely accurate, within .03% of the theoretical results. For percent difference of the catching up, we took the average experimental value and subtracted the individual value. Then, we divided it by the average value and multiplied by 100 to get a percentage. Our percentages were very small, thus demonstrating precision. There was one outlier where the blue car caught up at 230.96 cm, resulting in a percentage of 11.25%. This outlier may have been due to slow reaction time or improper readings of the meter stick. However,it can still be concluded that our results were very accurate and precise. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Discussion questions ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**﻿**In conclusion, our results turned out to be accurate. Each time that we performed a trial, the results ended up to be in some range of what we had originally predicted.For part A, our calculations showed that the two cars would meet and crash once the blue traveled 372. 321 cm and the yellow traveled 229.214 cm.For part B, our calculations showed that the faster, blue car would catch up with the slower, yellow car at the 260.156 cm mark. Since we used ramps, the cars were able to move in a straight line, thus giving us more accurate results. One of our sources of error found in our calculations was that for part A, instead of the two distances adding up to 600, it added up to 601. This was due to the fact that we used significant figures, thus truncating any "useless" decimals. Error could have also been found in the timing and reaction time. If we used another type of method to measure, like a USB to DataStudio, it could have been more accurate. Our percent error for part A was 0.57%. The percent difference ranged from -0.2% to 0.3% for the blue car and for the yellow car percents ranged from -0.55% to 0.55%. These values as well were very small. For Part B, percent error was 0.03 % and percent difference ranged from -0.2% to 1.95%, with an outlier at 11.35%. However, I believe the outlier was a human error. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> Overall, these percentages are very small, but could be improved. There are other evident ways to improve our data, but yet again our data is very precise. I believe our calculations couldn't have been that much closer to the actual values. If we were to improve the lab, I would say that it were required for each group to use the lab and a USB to get the most accurate results. Also, the lab could note that each car should be using a fresh pack of batteries. Therefore, everyone would be on the same page.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Part B: catching up **
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Where would the cars meet if their speeds were exactly equal?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The cars should realistically meet at 300 meters given that their speeds were exactly equal; this is the half way point.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">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.
 * 4) [[image:Screen_shot_2011-09-21_at_7.27.54_PM.png caption="crashing"]]
 * 5) [[image:Screen_shot_2011-09-21_at_7.28.00_PM.png caption="catching up"]]
 * 6) <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?
 * 7) [[image:Screen_shot_2011-09-21_at_9.38.47_AM.png width="385" height="355" caption="this is when the cars crash"]]
 * 8) [[image:Screen_shot_2011-09-21_at_9.42.36_AM.png width="465" height="241" caption="this is when the blue car surpasses the yellow car"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Conclusion **

=<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 27px;">**Accelerating/Decelerating Car Lab** = <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Ali and Caroline 9/14 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Hypotheses ** : A position-time (x-t) graph for increasing speed looks like a curve upwards, starting less steep and becoming steeper as time goes on. This is because it is covering a greater distance in less time. From a position-time graph, we can tell the velocity, because we can figure out the slope of the line.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">Objectives :**
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What does a position-time graph for increasing speeds look like?
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What information can be found from the graph?

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">**Available Materials** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Spark tape, spark timer, track, dynamics cart, ruler/meterstick/measuring tape <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">**Procedure** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Acceleration** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">We placed the car on the ramp, which was equipt with an inclination (due to one text book, shown). Therefore, this would make the car accelerated down the ramp. We attached a piece of spark tape to the car and put it through the spark timer. We then released the car until it was at the end of the ramp. Then, we collected the data by measuring the distance between the initial point to the final point, for each dot. The result is below. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Deceleration** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> We placed the car on the bottom of the the ramp, which was equipt with an inclination (due to one text book, shown). Therefore, this would make the car decelerate up the ramp (values would decrease because it went uphill). We attached a piece of spark tape to the car and put it through the spark timer. We then pushed the car up the ramp until it stopped. Then, we collected the data by measuring the distance between the initial point to the final point, for each dot. The result is below. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">**Data and Graph**

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Accelerating Data:Decelerating Data: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Analysis** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Interpret the equation of the line (slope, y intercept) and the R 2 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Both of our R values are VERY close to 100%. But, keep in mind, we used a polynomial trendline, rather than a linear trendline. Originally, when we used the linear trendline, our results were for increasing and decreasing were .92 and .88, respectively. Therefore, the polynomial trendline was a better choice because it was a curve.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">y= Ax<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">2 +Bx
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">y= distance& x= time
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">change in distance= 1/2at 2 + v i t
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">accelerating
 * Δd= 15.541t<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">2 + 11.795t
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">R<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">2 = 0.99996
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">decelerating
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Δd= -25.32t 2 + 90.698t
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">R<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">2 = 0.9999

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">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;">Find the average speed for the entire trip <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">**Discussion Questions** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">**Conclusion** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">﻿The results of this experiment proved our hypothesis to be successful. We hypothesized that the result of data would be plotted as a curve, and so it was. It seemed to be that as the car traveled along the ramp, speed was gained, and thus traveling greater distances in a smaller amount of time. Likewise, decelerating started off fast, but gradually slowed down, covering a less distance in a longer time. In this lab, there were a few sources of error. To start off, me and my partner did not start measuring at the first dot made by the spark timer. Thus, we had a false "initial velocity". This definitiley skewed our data, without us even thinking it done harm. It seems as if the car was already in motion, therefore accounting for this high initial velocity. Instantaneous velocity is supposed to be similar to the average speed, but as stated above, this was not accomplished by our data. Another source of error was most likely in our mathematical calculations; we may have calculated wrong or messed up numbers. Lastly, although our data was accurate, it was not as precise as it could have been. If we had been using something to hook up to the computer, our measurements would have been far more precise. However, this was not the case. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Overall, from this lab I learned that in a position-time graph lab, a curve will result from acceleration. The faster the object moves, the more distance covered in shorter periods of time, and the "steeper" the curve will become.
 * [[image:instanteanous.jpg width="320" height="240"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Increasing:
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">halfway= 6 cm/s
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">end= 5cm/s
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Decreasing:
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">halfway= 5.49 cm/s
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">end= 1.5 cm/s
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Accelerating
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Δd/Δt= 38.84 cm/s
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Decelerating
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Δd/Δt= 8.9375 cm/s
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What would your graph look like if the incline had been steeper?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">It would be a steeper curve, because the points would travel a greater distance in a shorter amount of time.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:STEEP.png width="268" height="211"]]
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What would your graph look like if the cart had been decreasing up the incline?
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The cart would start out going fast, with a steeper slope. It would then curve the opposite way, and gradually have a less steep slope.
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:DECREASE.png]]
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Compare the instantaneous speed at the halfway point with the average speed of the entire trip.
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> Accelerating instantaneous speed at the halfway point is 60 cm/s. For the average accelerating speed we had 38.84 cm/s. I believe that there is such a difference because the line that we used curved. There most likely was an error in calculation, as our values should have been close to that of the instantaneous speed.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?
 * 10) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">This makes sense because instantaneous speed is the speed that the object is moving during the specified time. Here, the tangent line intersects with one point out of the eighteen on the graph. Thus, by taking this point, we are figuring out velocity, which should be consistent throughout.
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">In class today we learned that the formula for some polynomial is y=Ax 2 + Bx. We learned that the A variable is 1/2 the acceleration (or in our case, 15.421, accelerating), while the B variable is initial velocity (again, in our instance, 11.795. )If you replace the variables with those from the acceleration equation, they turn out to be the same. The x axis can be exchanged with Δ<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">t, or the time value. The y variable can be replaced with Δd <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">because it is position.
 * 12) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
 * 13) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:v-t.jpg width="320" height="240"]]

=<span style="color: #9006ef; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;">Lab Acceleration of a Falling Body = <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif;">﻿Ali, Caroline 10/5 <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt; text-align: left;">**Objective**: <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 10pt; text-align: left;">What is the acceleration of a falling body? <span style="display: block; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt; text-align: left;">**Hypothesis**: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 10pt;">The acceleration of a falling body should be 9.8 m/s 2 or 981 cm/s 2. Hypothetically, the v-t graph should look like the following. Hopefully, the g from this graph will be 981 cm/s <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> 2 (referring back to the acceleration of a falling body). It should appear in our position time graph as the A value in Ax 2 +bx. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Materials ** : <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 10pt;"> Ticker Tape Timer, Timer tape, Masking tape, Mass, clamp, meterstick. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**Procedure** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: small;">For our lab, we took a spark timer, spark tape, masking tape, a weight, and dropped it off from a height. Dots were plotted for each interval of a second (.1,.2,...1). We then laid out the spark tape on the floor and measured the distance between each dot made by the timer by using a measuring tape. A picture of how we measured is shown below. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 10pt;">Above is the data for the position time graph, which compares the amount of time passed as the weight fell to the ground (measured in cm). <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The two images above show the data for the instantaneous velocity v. the mid time. Below is an example of how we found the instantaneous velocity. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"><span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">cm/s/s. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">We found the mid-time by taking the final and initial value and dividing it by 2. For example, MT= (0 s +0.1 s)/2 = 0.5 s.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Data and Graphs **

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Below is the percent difference of -5.98%. This is comparing the class average of 839.417 cm to our average of 889.65 cm. This percentage is very small and is within the "20 percent range" concept we created for accuracy. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 17px;">Sample Calculations **

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Below is the percent error of 9.31. It is comparing the theoretical value of 981 cm/s/s to our experimental value of 889.65 cm/s/s. The percent is very small and is within the "20 percent range" concept we created for accuracy. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 14px; line-height: 24px;">Below is an example of how we found the velocity for a given point. <span style="font-family: arial,helvetica,sans-serif;">
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 17px;">Analysis **

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">To begin, we found that the polynomial equation y=Ax2+Bx happens to come from the equation d=1/2at2+vit; therefore, A=1/2acceleration and B=initial velocity. Additionally, y=mx+b can be derived from the equation Vf= at +Vi. These factors will later be discussed throughout the analysis. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">For the position-time graph, the trend is a polynomial one, indicated by the equation of the line (y=445.35x<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">2 +50.138x). In this case, the acceleration is 445.35 and the initial velocity was 50.138. Our R2 value was extremely accurate at 1, showing that we had great results. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The velocity time graph, unlike the p-t graph, was a linear function (y=889.65x+50.91). In this case, slope=889.65 and B=50.91. Our R2 value was extremely accurate with a value of 0.99994. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">For both graphs, we got an initial velocity that was not zero as expected because we may have had a delayed reaction when dropping the weight, after the ticker tape was already turned on. According to the original equation, 1/2A equals 445.35. Technically, this should mean that the value 445.35 cm from the p-t graph, doubled, should equal our slope of the velocity time graph. Although not an exact fit, the value almost equals 889.65 cm/s/s, as it equals 890.7 cm/s/s. Thus, we can conclude it is accurate. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Conclusion ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Our results turned out to be very accurate. Our hypothesis was partially correct. We believed that the value of our accelerating object should be about 981 cm/s/s. As we found from our percent error, our calculation was relatively accurate, with a percent of 9.31%. However, we originally thought that the v-t graph would ride in the fourth quadrant and be negatively sloped away from the origin. However, since we truncated the negative values, the v-t graph was in a positive direction. We were correct in believing that the accelerating "g" value would come from the A value in the position-time graph, which is shown in the data section above. <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif;">Our lab, although very accurate, contained some sources of error. Again, or value of percent difference from the class average was -5.98%, while the percent error from the g value of 981 cm/s/s turned out to be 9.31%. This error could have been found in rounding and determining measurements. Since we used a tape measure "taped" to the ground (as was the ticker tape), it may have shifted slightly as we were recording. Another source of error was the fact that the spark tape was rubbing through the spark timer, causing friction. This may have delayed the amount of time between each dot and skewed our data. <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif;">A way to change the lab in favor of all of the lab groups would be to alter the tactic of tracking the time between each dot. If there were a more accurate way to record the position of a weight over time, such as an electronic device that rids free of friction, it should be used. <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif;">In conclusion, our experiment was successful!
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">Discussion Questions **
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Does the shape of your v-t graph agree with the expected graph? Why or why not?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">No, the expected graph was a constantly sloped line in the negative direction moving away from the origin. This is because we omitted the negatives when counting our results.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Does the shape of your x-t graph agree with the expected graph? Why or why not?
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Yes, we expected the graph to be a polynomial--gradually increasing as time passed. It completely matches up with our expected graph, a J curve.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">﻿[[image:classavg.png width="112" height="159"]][[image:percent_difference.png]]
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Our results confirm that our data is very accurate. Again, our data was in the "20 percent range". The class average was 839.417 cm/s/s, which clearly is a lower value than ours. As you can see in the data set, most values resided in the seven and eight hundreds. However, there were a few outliers at 1225.4 cm/s/s and 659.39 cm/s/s, which skewed our average.
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Did the object accelerate uniformly? How do you know?
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Yes, because in the V-T graph there is a constant slope. As shown in the graphs in the data section above, acceleration is almost exactly uniform as there is almost a constant slope shown in the linear trendline. We know this because the slope of the velocity time graph infact equals acceleration.
 * 10) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">In our lab, it was hard to make gravity the only factor. Being that we are in a high school, equipment such as a vacuum is not easily accessible. In this experiments, factors that could have been a cause to increase acceleration to be higher than it should be were the density of the weight and the factor of air pressure. Contrary, the effect of friction could have caused acceleration to be lower than it should be.

=<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 27px;">Activities =

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;"> **9/12**

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Constant Motion (slow and Fast) and at Rest Graphs**
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Graph 1 X-T: where are you located? slope=speed <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Graph 2 V-T: how fast are you going? negative= going towards/backwards; slope=acceleration area=displacement <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Graph 3 A-T: what is the change in velocity?= area under the graph <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**at rest:** standing still. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**constant speed:** covers a distance at a rate. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**fast constant speed:** covers large distances. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**slow constant speed:** covers small distances. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">accelerating graph: **<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">distance increases between the points.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">decelerating graph: **<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">distance decreases between the points.

<span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">How can you tell that there is no motion on a… <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">How can you tell that your motion is steady on a… <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">How can you tell that your motion is fast vs. slow on a… <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">How can you tell that you changed direction on a… <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">What are the advantages of representing motion using a… <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">What are the disadvantages of representing motion using a… <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Define the following:
 * 1) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">position vs. time graph
 * 2) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">it is at the starting point
 * 3) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">velocity vs. time graph
 * 4) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">horizontal line at zero
 * 5) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">acceleration vs. time graph
 * 6) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">horizontal line at zero
 * 1) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">position vs. time graph
 * 2) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">it will be a constant slope
 * 3) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">velocity vs. time graph
 * 4) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">it will be a horizontal line
 * 5) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">acceleration vs. time graph
 * 6) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">it will be a horizontal line
 * 1) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">position vs. time graph
 * 2) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">steeper slope indicates a faster moving object
 * 3) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">velocity vs. time graph
 * 4) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">y value of the line would be greater for the faster moving object than the slower one
 * 5) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">acceleration vs. time graph
 * 6) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">the speed stays the same so there is no acceleration --> keeps it at zero
 * 1) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">position vs. time graph
 * 2) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">the slope will become negative once you turn around, but positive if it were previously negative
 * 3) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">velocity vs. time graph
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">reaches zero and decreases under x-axis
 * 5) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">acceleration vs. time graph
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">only shows the change in speed; does not show direction
 * 1) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">position vs. time graph
 * 2) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">it shows direction, gives intervals of time, and has a slope
 * 3) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">velocity vs. time graph
 * 4) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">slope shows the increase/decrease in velocity
 * 5) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">acceleration vs. time graph
 * 6) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">given that there is a change in speed, slope shows this change
 * 1) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">position vs. time graph
 * 2) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">acceleration is not shown
 * 3) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">velocity vs. time graph
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">this takes into account displacement, not total distance
 * 5) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">acceleration vs. time graph
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">only shows changes within the speed but doesn't show velocity
 * 1) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">**No motion:** when the object is at rest; velocity, position, and speed are at zero
 * 2) <span style="color: black; font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Constant speed:**when the object is moving at a constant rate; a constant distance is covered in the same amount of time, no matter the interval.

=<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 150%;">Notes = <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">﻿**Kinematics: study of motion**

<span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Constant Speed**
<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**<span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif;">Types of Speed ** <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif;">average speed= total distance/ total time==> can also be found if you know two different speeds.. you avereage them together! <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif;">constant speed--> not changing, the instantaneous speed is always the same for the time interval (time is really small) <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Types of Motion** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">acceleration: changing speed; involves increasing and decreasing speeds
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">at rest
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">constant speed
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">increasing speed
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">decreasing speed

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Motion and Ticker Tape Diagrams**
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">when at rest (v=0; a=0) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">when at constant speed
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">﻿show direction of velocity
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">the direction of the arrows change depending on the direction (right left up down)

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">when increasing speed <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">when decreasing speed <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">﻿{.} at rest <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;"> ---> ---> ---> --- <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">﻿> (a=0)
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">--->-->--->
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">---> (a)
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">-->--->--->
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"><(a) (negative value)
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">Ticker Tape **

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">*draw back to this*: ticker tapes dont show directions; but can be easily used when you need to take measuresments <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Signs are Arbitrary**
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">depends on the situation, depends which way it points

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Graphs at Rest and at Constant Speed Examples
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">**Acceleration**
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">(a) m/ s (squared)
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">V= Δd/ Δt (only for average or constant speeds)
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">V= (Vi +Vf)/2 (only for average speed)

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">**FIVE KINEMATICS EQUATIONS**
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">a= Vf- Vi/ Δt <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Vf= Vi +aΔt (no displacement <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Δd= 1/2( Vi + Vf)t <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Δd= Vit + 1/2at(squared) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Vf(squared)=Vi(squared)+2aΔd

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Increasing and Decreasing Speed Graphs
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">



**<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;">Interpreting Position Time Graphs (E,F,G) **
<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;">E. <span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;">F. <span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;">G.

<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;">**Free Fall**

 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">﻿only gravity is acting on object and no other forces
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">ignoring air resistance
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">ie: dropping something, the instant it is dropped to the time it hits the ground is free fall
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:Photo_on_2011-10-03_at_09.43.jpg width="320" height="240" caption="EXAMPLE"]]
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:Photo_on_2011-10-11_at_09.12.jpg width="320" height="240" caption="example of freefall"]]

=<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 150%;">Homework =

<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">9/8 (Lesson 1: 1D Kinematics)

 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%; line-height: 26px;">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%; line-height: 26px;">Displacement was one of the topics that I understood well from our class discussion. It simply is the combination of distance traveled from the starting point, plus direction—aka the overall change of position
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Speed v. Velocity. This concept I understood because to me, velocity : displacement :: speed : distance. Speed is the rate at which something moves, to matter the distance. Velocity, however, takes into account displacement. If an object moves ten feet forward and ten feet back in 20 seconds, the velocity will be zero; however, the speed will be 1 ft/sec.
 * 4) <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.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I was not clear about scalars when I first read it. I didn’t even know what the term was, so it struck me. But now, I can tell that it is just the magnitude alone (which I know because of Precalc last year). It is simply one quantitative value.
 * 6) <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.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I do understand everything that I read.
 * 8) <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?
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">I did not know of scalars. I only knew of vectors from last year in Precalc.

<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">9/9 (Lesson 1: 1D Kinematics)
>>
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">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: 12px;">Ticker tape. I understood the concept, that the faster an object is moving, the more space there is in between each dot. Vice Versa.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">Motion diagram. I understood this concept in class. It is simply a visual aid to depict how fast/slow an object is moving, as well as what direction it is moving in.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">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.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">I was unclear about how to show an accelerating object. But after the reading, I understood that accelaration could be clearly shown by a cluster of dots that spreads out, or vice versa. Below is a picture that demonstrates this concept.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">I do understand everything that I read.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">What (specifically) did you read that was not gone over during class today?
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">I knew of everything, as we went over it in class.

<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">9/13 (Lesson 2 1D Kinematics)

 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">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: 12px;">Acceleration is a vector quantity that is defined as the rate at which an object changes velocity. If it's velocity changes, then it is accelerating.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">Constant Acceleration is when it changes its amount by the same amount, each second.An object that is constantly changing its velocity is an accelerating object--but not at constant acceleration.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">[[image:Screen_shot_2011-09-13_at_9.31.34_AM.png width="306" height="140"]]
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">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.
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">I was not clear about calculating the Average Acceleration. But, the equation below from the physics classroom helped me understand more easily.
 * 7) [[image:Screen_shot_2011-09-13_at_9.33.23_AM.png width="239" height="42"]]
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">I do understand everything that I read.
 * 10) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">What (specifically) did you read that was not gone over during class today?
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">I did not know of Average Acceleration.

<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">9/15 (Lesson 3&4: 1D Kinematics)
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Lesson 3 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px; line-height: 18px;">Lesson 4
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">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;">Ticker Tape Diagrams I already understood well from all of the labs that we have completed recently. As the object is accelerating, the spaces increase between the dots. Likewise, the spaces decrease between the dots when the object in motion are decelerating.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Vector Diagrams include an aspect that ticker tape diagrams cannot. They show direction of the object AND direction of acceleration. Vector diagrams are used more with velocity, whereas ticker tape diagrams are used with speed.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">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.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">To be honest, there was nothing in this section that I did not understand. The concept is fairly simple, especially since we have gone over it multiple times.
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">I do understand everything that I read.
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">What (specifically) did you read that was not gone over during class today?
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">:) Nada!
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">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;">I already understood the meaning of the shape of a position-time class. The activity that we did in class involving the motion sensor helped me understand that when an object is at a constant, positive velocity, the p-t graph will look like a straight line. However, if the velocity changes, it will become a curved line.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Essentially, slope= velocity, in ALL circumstances when looking at a p-t graph. Therefore, displacement is definitely accounted for. As the slope goes, so goes velocity!
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">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.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">There really wasn't anything in the reading that wasn't gone over thoroughly in class. I feel confident in this topic.
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">What  did you read that you still don’t understand? Please word these in the form of a question.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">I do understand everything that I read.
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px;">What (specifically) did you read that was not gone over during class today?
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Everything has been covered in the past few days or so.

<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;">**10/3 Lesson 5 Method 1**
<span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 130%;">Free fall is an object that falls, with the only force acting upon it being gravity. All objects, despite the mass, will fall at the same rate given that it is in a vacuum. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Introduction to Free Fall ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">A free falling object is an object that is falling under the sole influence of gravity. There are two important motion characteristics that are true of free-falling objects:
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Free-falling objects do not encounter air resistance.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (10 m/s/s)

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The dot diagram at the right depicts the acceleration of a free-falling object. If distance is increasing it is a sign that the ball is speeding up as it falls downward. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** The Acceleration of Gravity ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">9.8 m/s/s is known as the ** acceleration of gravity ** - the acceleration for any object moving under the sole influence of gravity. The symbol ** g ** denotes it. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Representing Free Fall by Graphs ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">A position versus time graph for a free-falling object is shown below. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">A velocity versus time graph for a free-falling object is shown below. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">*The velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen* <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> The formula for determining the velocity of a falling object after a time of ** t ** seconds is ** v **** f **** = g * t ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Example Calculations: ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">At t = 6 s v f <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">(9.8 m/s 2 ) * (6 s) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">58.8 m/s

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">At t = 8 s v f <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">(9.8 m/s 2 ) * (8 s) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">78.4 m/s <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The distance fallen after a time of ** t ** seconds is given by the formula= ** d = 0.5 * g * t **** 2 ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Example Calculations: ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">At t = 1 s d = (0.5) * (9.8 m/s 2 ) * (1 s) 2 = 4.9 m <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">At t = 2 s d = (0.5) * (9.8 m/s 2 ) * (2 s) 2 = 19.6 m <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">At t = 5 s d = (0.5) * (9.8 m/s 2 ) * (5 s) 2 = 123 m (rounded from 122.5 m) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** The Big Misconception ** Free-fall is the motion of objects that move under the sole influence of gravity; free-falling objects do not encounter air resistance. More massive objects will only fall faster if there is an appreciable amount of air resistance present. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">All objects accelerate at the same rate involves the concepts of force and mass. The greater force on more massive objects is offset by the inverse influence of greater mass. Subsequently, all objects free fall at the same rate of acceleration, regardless of their mass.

=<span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 27px;">Egg Drop Project = <span style="color: #6920d9; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 27px;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Description** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Our final project had a parachute attached by a string to a cone, made of newspaper. Inside, there were strips of crumpled paper. Along the sides to provide cushioning were straws. Also, at the tip of the cone, we stuffed newspaper and two paperclips. This, hopefully, would provide some weight and some distance between the egg and the crash area. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Results** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Our egg cracked a tiny bit from the crash. It was mostly protected from the force (stopping) because of the cushioning at the bottom of the cone. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**Analysis** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Originally, our project had been a square shape crate that held the egg in the center. Since the egg jumped out of this contraption, we decided to start over. We then moved onto the cone model, and added straws to provide cushioning. On our final prototype, we added two more straws for cushioning. Finally, when we dropped our project, we had hoped that the parachute would provide some air resistance so that it would be an easy fall. As it fell, the parachute gave way. But, in result, our egg was mostly safe, aside from a tiny crack. The cushioning at the bottom of the cone most likely created a better crash zone, preventing the egg from smashing. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Our result was that our cone moved at a velocity of 5.55 m/s. It's acceleration was 7.26 m/s2. Below is our calculation of how we got acceleration. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 110%;">**What would we do to fix it?** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">To fix our project, we most likely would have made a larger surface area on the parachute in ration to the size of the cone. We could have also taken out some of the paper clips to reduce the weight. In my opinion, was a smart move for us to go from a box to a cone. = =