Group+6.1-4-EB

Alyssa Berger, Nikki DeGisi, Samantha Cheng
 * Lab: Bombs Away** 9/29/10

**Purpose**: What is the acceleration of a falling body?

**Hypothesis**: If we run a spark tape through a timer and there is a free-falling mass is attached, then we will find the acceleration of gravity by using a position-time graph. This doesn't answer the purpose...

a) Set up this experiment by attaching a ticker tape timer to a clamp, and then attaching the clamp and ticker tape timer to the top of an open cabinet. b) Materials needed for this experiment: Ticker Tape Timer, Timer tape, Masking tape, Mass, clamp, and a meter stick. c) Place a long piece of ticker tape through the ticker timer, and attach a mass to the front of the tape. Turn on the ticker timer to 60 hertz, and as the timer is turned on, drop the tape and weight and allow for the tape to freely fall so there are no interferences and it can be marked up properly. Tape the ticker tape to the table. Count the number of dots on the tape, and measure the distance of each dot from the beginning of the tape. Record this data on Excel, use the data to create a graph. Find the acceleration of the ticker tape by graphing a distance v. time graph.
 * Procedure for lab**:

nice graph! Great measuring!
 * Position v. Time Graph: [[file:FreeFallLabGraph.xls]]**

missing analysis of equation of curve

1. Does the shape of your graph agree with the expected graph? Why or why not? Yes, the graph of the experiment corresponds to the expected graph. As the object moves farther from the ticker tape timer, the distance increases, but at a faster and faster pace. Naturally, this causes an upward curve, which shows increasing velocity. Position is changing at a faster pace. An increasing velocity signals that there is acceleration. Because ticker tape timers do not show direction well, and distance was measured from the ticker tape timer, gravity's acceleration of -9.8m/s^2 must be shown through a positive change in distance. Therefore, the graph curves upward.
 * Discussion Questions:**

2. How do the results compare to that of the class? where are class results? The results were fairly close.

percent difference = abs(my value-other value)/average of both = abs(879.34-874.46)/876.9 = .00557 = .557%

Our results were very precise. The acceleration we calculated is very, very close to the acceleration the class generally calculated.

3. Did the object accelerate uniformly? How do you know? Yes, the object had accelerated uniformly. This is known due to the fact that the weight was accelerating from the constant force of gravity. Because objects in free fall are influenced by the constant force of gravity, the object accelerates uniformly. Yes but how do you know from your graph?

4. What should the velocity-time graph of this object look like? The velocity- time graph of this experiment should have an increasing line with a positive slope. what is an "increasing line"?

5. Write down the expected equation of the line from this v-t graph (use specific information from your x-t graph). The y-intercept of a v-t graph made from this p-t graph is expected to be zero because at zero time, the object was not moving yet. The slope of a v-t graph is its acceleration, which for this experiment we would expect to be 980 (not 9.8 because we measured in centimeters, not meters). However, in the case of using the numbers from our p-t graph to solve for acceleration, a came out to 879.34. Thus, the equation of the line on a v-t graph from our p-t graph would be y=879.34x good

6. What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be? Acceleration due to gravity might be higher or lower than 980cm/s^2 if the distances were not measured correctly. measuring incorrectly is not a valid source of experimental error If the distances were measured as being larger than they were, this would cause acceleration to be higher than it should be. It would appear that the velocity was changing at a greater rate if the distances were seemingly larger, making the acceleration larger than it should be. Likewise, if the measurements were smaller than they should be, it would seem that the velocity was changing slower than it really was. Also, acceleration would be higher if the mass was pulled downward by another force besides gravity during the experiment. <-- like what? It would also be slower if the tape was stuck in any way and stopped.<-- you are being so vague!!!


 * Conclusion:**

unify your font please! The equation of our line was essentially the equation d = v(1)t + 1/2at^2. The x^2 term from the equation of our line could be put in this equation in front of the t^2 as 1/2a. So, to solve for acceleration we multiplied the number in front of x^2 (439.67) by 2 and found this to be acceleration. That number was 879.34 cm/s^2, which is almost 100 cm off from the actual acceleration of gravity, which would be 980 cm/s^2. Although our theoretical and experimental values are not the same, the percent error is low enough that we can see that the acceleration of the object was indeed caused by the acceleration of gravity. Our acceleration is not perfect due to errors made while completing the experiment.

=
Error is likely to have occurred in measuring the distance of each dot. The last digit of our distances is uncertain because we had to estimate to the nearest hundredth centimeter instead of using millimeters. If measurements are not exact, the points on the graph will all be a little bit off, ultimately causing the equation of the line not to be exact either. I disagree. You measured to a hundredth of a centimeter. This is pretty precise. Besides your R^2 value was 1.0!  Because the numbers in our equation were off, we were then not able to find the exact acceleration when we plugged the number into another equation to solve for a. Another possible source of error is friction when the tape was running through the timer. The tape must still make contact with the timer (the spark); therefore, that contact will result in some friction. Friction will cause the tape to run through more slowly than the force of gravity alone would cause it to. ======

% Error = abs[.11447] X 100
<span style="color: #000000; font-family: 'Times New Roman',serif;">% Error = 11.447 % <span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">Calculations belong above in analysis section. The conclusion is a place where you summarize or recap your results. To address this inherent source of error in the lab, we could perhaps use a more exact measuring tool <span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">like what? , a much longer piece, or both. With a more exact measuring tool, the second decimal values that we had to estimate, could be measured exactly. With a much longer piece of tape, the ticker tape timer could be set to 10 hertz, rather than 60 hertz. The lab currently uses 60 hertz, because it will provide more dots, as the tape quickly falls through the device. With a much longer piece of tape, we can still get a similar number of dots, but much more spaced out from one another. The benefit of that space, is that it allows us to measure the dot more easily, than if the dots were all close together, a case that causes the tiniest misreading to alter a graph. <span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">interesting thought Gravity is a major source of acceleration that is constantly present on the earth. All objects feel the force of gravity, and any falling object will be influenced by an acceleration of -9.8m/s^2. It is important for us to understand that this force exists, and affects any object with that constant acceleration. We increase that understanding by performing this lab, and measuring gravity's acceleration. <span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">these last 4 sentences are unnecessary

<span style="font-family: Arial,Helvetica,sans-serif;">**Lab**: A Crash Course in Velocity, 9/24/10

**Purpose:** The purpose of Objective 1 is to be able to find the velocity of an object by making a distance v. time graph after finding ourselves the distance and time by using a spark timer. The purpose of Objective 2 is to find a point of intersection for two objects moving at different velocities in opposite directions towards each other and to be able to find that point of intersection on a distance v. time graph. The purpose of Objective 3 is to find the point at which a fast moving vehicle would catch up with a slow moving vehicle and to see if we can find this point graphically on a distance v. time graph. We also need to be able to solve Objectives 2 and 3 algebraically.

**Hypothesis:** If we run a constant motion vehicle at a fast pace and one at a slow pace and take a spark diagram, then we will be able to find the velocities by graphing a position-time graph and finding the slope. The slope of the line of our fast car will be steeper than the slope of the slow car because it will travel a greater distance over a shorter period of time. When we run the catch up experiment, it will take a short amount of time for the fast car to catch up with the slow one. When we run the crash experiment, the cars will crash closer towards the slow moving vehicle.

**Procedure for** ** Spark Tape Diagrams and Distance v. Time Graph ** a) Set up this experiment by taping about a meter of spark tape to both the slow and fast motion vehicle. b) Materials needed for this experiment: a slow constant motion vehicle, a fast constant motion vehicle, tape measurers or meter stick, spark timer, spark tape, and masking tape c) Put the spark tape all the way through the timer. Set both timers to 10 hertz, or 10 dots per second. Start the timers and then the cars, making sure that there is nothing in the car's paths. Create a spark diagram for the cars. You know the time between each dot is .1 second, and to graph the diagrams, you must also find the distance between the dots. Make sure the distance is equal between all dots and the car did not start or stop during the trial. From the beginning of the diagram, pick how many points you would like to plot on your graph (we chose to plot 10 points). The x-value is time. The y-value for your coordinates is the distance from the first dot at that time. Make sure to measure distance accurately. Put the points on an Excel spreadsheet. Highlight your points and create a graph, one line for the slow moving vehicle and one for the fast moving vehicle. Use the Excel program to create a trendline and find the slope and R^2 value of each line. The slope of each line is the velocity (cm/s) of each car. The R^2 value reflects the percentage of points on your graph that fit onto the trendline.

<span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">very nice graph! Great results. 1) Set up a tape measure that creates a 600 cm or 6 meter gap between the slow car and the fast car. 2) Materials needed: a slow moving and fast moving car, a tape measure 3) Turn on both of the cars and the same time. Record when the cars collide into each other, how long it took, and the distance each vehicle travelled to get there. We solved it mathematically to get exact results and then graphed the results to see what occurred visually.
 * Distance v. Time Graph:** [[file:DistancevTime2.xls]] <span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">include screenshot of data table please
 * Series1 is the line for the slow constant motion vehicle and Series2 is the line for the fast constant motion vehicle.
 * Procedure for Experiment 1:**

<span style="font-family: Arial,Helvetica,sans-serif;">**Experiment 2:** <span style="font-family: Arial,Helvetica,sans-serif;">In this experiment, we aligned a fast moving vehicle 1 meter away from a slow moving vehicle. We had to observe how long it would take for the fast car to catch up to the slow car if they were both turned on simultaneously. There were common trends in our results, and to find the exact distance of the cars as well as the time it took for the fast vehicle to catch up to the slow vehicle, we solved it mathematically. <span style="font-family: Arial,Helvetica,sans-serif;">**Procedure for Experiment 2:** <span style="font-family: Arial,Helvetica,sans-serif;">1) Set up this experiment by laying a tape measure down along the floor and putting the slow moving car at least one meter ahead of the fast moving car. <span style="font-family: Arial,Helvetica,sans-serif;">2) Materials needed: tape measure, slow moving vehicle, fast moving vehicle <span style="font-family: Arial,Helvetica,sans-serif;">3) Turn on both of the cars at the same time, and when the fast car eventually reaches the slow car, observe on the tape measure where the chase ends and record that number. Run a trial for this at least 3 times. Then, mathematically solve for the time it had taken for the car to catch up to the other and its distance.

__**DATA FOR EXPERIMENT 2:**__

<span style="font-family: Arial,Helvetica,sans-serif;">Velocity of fast car= 32 cm/second <span style="font-family: Arial,Helvetica,sans-serif;">Velocity of slow car= 10 cm/ second

<span style="font-family: Arial,Helvetica,sans-serif;">Vs= d2/ t2 <span style="font-family: Arial,Helvetica,sans-serif;">10= d2/t2 <span style="font-family: Arial,Helvetica,sans-serif;">10t2=d2

<span style="font-family: Arial,Helvetica,sans-serif;">Vfc= d1/t1 <span style="font-family: Arial,Helvetica,sans-serif;">32= d1+100/ t1 <span style="font-family: Arial,Helvetica,sans-serif;">32t= d1 + 100 cm <span style="font-family: Arial,Helvetica,sans-serif;">22t= 100 <span style="font-family: Arial,Helvetica,sans-serif;">22t/22= 100/22 <span style="font-family: Arial,Helvetica,sans-serif;">t= 4.5 seconds

<span style="font-family: Arial,Helvetica,sans-serif;">10t=d2 <span style="font-family: Arial,Helvetica,sans-serif;">10(4.5)= d2 <span style="font-family: Arial,Helvetica,sans-serif;">45= d2 <span style="font-family: Arial,Helvetica,sans-serif;">45+100= 145 cm= d <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11px; line-height: 16px;">1

__**TRIALS**__

Car Collision Experiment Average: 169 Percent Error:
 * Trials || Position of Collision from Slow Car (0cm) ||
 * Trial 1 || 150cm ||
 * Trial 2 || 178cm ||
 * Trial 3 || 178cm ||
 * Trial 4 || 170cm ||

= [abs(169-146)/146]*100 = 15.7% error

__Car Catching Up Experimen__t
 * Trials || Position where vehicles caught up ||
 * Trial 1 || 120 cm ||
 * Trial 2 || 110 cm ||
 * Trial 3 || 130 cm ||
 * Trial 4 || 120 cm ||

Average: 120 Percent error: =[abs(120)-(145)/(145)] *100= 17.2% error

<span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">Good work, although formatting is a little confusing. Different fonts, mixed-up order, different methods of presenting data.... Try to unify final product. Maybe assign one of the group to do the final proofreading (rotate this chore each lab?).

<span style="font-family: Arial,Helvetica,sans-serif;">1. Why is the slope of the position-time graph equivalent to average velocity? <span style="font-family: Arial,Helvetica,sans-serif;">2. Why was it okay to set the y-intercept equal to zero? <span style="font-family: Arial,Helvetica,sans-serif;">3. What is the meaning of the R2 value? <span style="font-family: Arial,Helvetica,sans-serif;">4. Where would the cars meet if their speeds were exactly equal? <span style="font-family: Arial,Helvetica,sans-serif;">5. 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?
 * Discussion Questions:**
 * <span style="font-family: Arial,Helvetica,sans-serif;">The slope of a position-time graph is average velocity because of what the coordinates represent. The x-coordinate is time, and the y-coordinate is distance. The object's slope would be calculated as y2-y1/x2-x1, or change in distance/ change in time. Change in distance/change in time is the formula that gives you velocity. Therefore, the line's slope is equal to its average velocity.
 * <span style="font-family: Arial,Helvetica,sans-serif;">To solve for a y-intercept, you set x equal to zero. It was okay to set the y-intercept equal to zero for the distance v. time graph because when x (time) was zero, y (distance) was also zero because the vehicles were in their starting positions and had not moved any distance.
 * <span style="font-family: Arial,Helvetica,sans-serif;">The R2 value represents the trend-line. Microsoft excel is able to determine a line that "best fits" the points created. Using he time values and position values plotted, the program creates a line that best accommodates and represents the general trend or slope of the graph. This line is useful in allowing the person reading the graph to better understand what motion is occurring.
 * If their speeds were equal, the two cars would meet exactly in the middle of their starting points, and each will travel an equal distance of 300cm to that point.


 * COLLISION**

<span style="font-family: 'Times New Roman',Times,serif;">Carf has velocity of 32cm/s <span style="font-family: 'Times New Roman',Times,serif;">Cars has velocity of 10cm/s <span style="font-family: 'Times New Roman',Times,serif;">df + ds = 600cm

<span style="font-family: 'Times New Roman',Times,serif;">Vf= df / t <span style="font-family: 'Times New Roman',Times,serif;">32 = df / t <span style="font-family: 'Times New Roman',Times,serif;">32t = df

<span style="font-family: 'Times New Roman',Times,serif;">Vs = ds / t <span style="font-family: 'Times New Roman',Times,serif;">10 = (600 – df) / t

<span style="font-family: 'Times New Roman',Times,serif;"> 10t = 600 – 32t <span style="font-family: 'Times New Roman',Times,serif;">42t = 600 <span style="font-family: 'Times New Roman',Times,serif;">t = 14 s

<span style="font-family: 'Times New Roman',Times,serif;">df = (32)(14) <span style="font-family: 'Times New Roman',Times,serif;">df = 454 cm

<span style="font-family: 'Times New Roman',Times,serif;">ds = 600 – 454 = 146cm

<span style="font-family: 'Times New Roman',Times,serif;"> The two cars collide after 14 seconds. The fast car travels 454cm, while the slow car travels 146cm.


 * CATCHING UP**

<span style="font-family: 'Times New Roman',Times,serif;">tf = ts <span style="font-family: 'Times New Roman',Times,serif;">df = ds +100

<span style="font-family: 'Times New Roman',Times,serif;">Vs = ds/t <span style="font-family: 'Times New Roman',Times,serif;">10 = ds/t <span style="font-family: 'Times New Roman',Times,serif;">10t =ds

<span style="font-family: 'Times New Roman',Times,serif;">Vf = df/t <span style="font-family: 'Times New Roman',Times,serif;">32 = (100+ds)/t <span style="font-family: 'Times New Roman',Times,serif;">32t = 100 +10t <span style="font-family: 'Times New Roman',Times,serif;">22t = 100 <span style="font-family: 'Times New Roman',Times,serif;">t = 4.55

<span style="font-family: 'Times New Roman',Times,serif;">ds = (10)(4.55) <span style="font-family: 'Times New Roman',Times,serif;">ds = 45

<span style="font-family: 'Times New Roman',Times,serif;">df = 100 +ds <span style="font-family: 'Times New Roman',Times,serif;">df = 100 +45 <span style="font-family: 'Times New Roman',Times,serif;">df = 145

<span style="font-family: 'Times New Roman',Times,serif;">The fast car catches up to the slow car after 4.55 seconds, at 145cm from the fast car's starting point.

At the point (4.55, 145), the two lines collide. This was when the fast moving vehicle had caught up to the slow moving vehicle.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 24px;">6. 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? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 24px;"> It is not possible to find the points where they are at the same place at the same time. The cars were each at a constant, different velocity, so it will never show when the fast car caught up to the slow vehicle. <span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">very nice graphs and explanations!


 * Conclusion**

The experiment was successful in comparing (both physically and graphically), the motion of two objects at different speeds. Our hypothesis was correct. We were able to use a position-time graph to find velocities for the fast and slow car, through the Microsoft excel program. Then, progressing into the next stages of the experiment, we found that our predictions for both scenarios were accurate. The fast car was able to catch up the slow car fairly quickly, because of a disparity of 22cm/s velocities. In the collision portion, the fast car collided closer to the starting position of the slow car. The fast car covered 454 cm and the slow car covered only146 cm, before the two collided.

Naturally, our experiment was subject to potential errors. With initial measurements of velocities using ticker tape, there were times when the car may have gotten stuck, or the machine could have stuttered. Technology is always a possible victim of malfunctions. More likely though, the sources of error lied <span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">lay in the execution of the catching up and collision problems. No matter how aligned the cars were when we tried to run the experiment, the cars often attempted to change direction, not traveling in the direct path we would want it to. <span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">annoying, isn't it? Therefore, the point of collision or catching up between the cars could have been later than if the cars had moved in the perfect straight path. Furthermore, especially with the catching up problems, where the two cars would continue moving, it is difficult to determine the exact moment when the two cars are side-by-side, and see the measurement on the measuring tape.

While these errors were in inherent in the lab, there are possibilities to diminish their effect in the results. Perhaps, if there were some way to hold the cars in perfect direction, the data would be more accurate. Also, if there were a means of capturing the exact moment of collision or catching up, then the numbers in the calculations would no longer represent that potential error. If we could somehow snapshot that moment to see where the cars were on the measuring tape, that would allow our numbers to be more accurate.

While we were only using miniature cars, this type of motion is extremely common in everyday life. On the roads, we see cars of faster velocities catch up to cars of slower velocities, and we see motions of all different speeds along side one another very often. While the least lab familiarized us with representations of motion, this lab is necessary in furthering our understanding of motion in comparison with other types of motions (motion of different velocities and distances). Then, the calculations that accompany these problems correlate with our recent introductions to “Catching up” problems and “collision” problems, where we must calculate the conditions of the scenario.

<span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive; font-size: 120%; margin: 0px 0px 0in; padding: 0px;">well-said. Although all is good in the conclusion, FYI: you don't have to do both parts of implication, you can choose either method for fixing errors OR application.

**Objective:** What are the different types of motion? What is the best way to represent the motion?
 * Lab**: Representations of Motion

<span style="font-family: Arial,Helvetica,sans-serif;"> **HYPOTHESES**:

<span style="font-family: Arial,Helvetica,sans-serif;"> **Distance, Velocity, and Acceleration v. Time Graphs** <span style="font-family: Arial,Helvetica,sans-serif;"> If we move towards/away from a motion detector and either keep a constant speed, increase speed, or decrease speed, then the graphs will reflect the changes in speed and position. Each of the three graphs should all relate because they are connected by time.

<span style="font-family: Arial,Helvetica,sans-serif;"> **Ticker Tape** <span style="font-family: Arial,Helvetica,sans-serif;"> If the tape is pulled towards/away from yourself and the speed is either constant or changing, then the dots will be closer together at a slow speed and further apart at a greater speed, reflecting only the speed of the tape and not the direction.

<span style="font-family: Arial,Helvetica,sans-serif;"> **PROCEDURES:**

Materials: ticker tape, ticker tape timer

<span style="font-family: Arial,Helvetica,sans-serif;"> Ticker Tape Diagrams <span style="font-family: Arial,Helvetica,sans-serif;"> a) Put a piece of the ticker tape no longer than a foot in the ticker tape machine. <span style="font-family: Arial,Helvetica,sans-serif;"> b) Materials you will need for ticker tape graphs: ticker tape, ticker tape timer <span style="font-family: Arial,Helvetica,sans-serif;"> c) Pull the tape through the ticker timer either: <span style="font-family: Arial,Helvetica,sans-serif;"> to increase motion: pull the tape through with increasing speed (either away or towards yourself) <span style="font-family: Arial,Helvetica,sans-serif;"> to decrease motion: pull the through with less and less speed (either away or towards yourself) <span style="font-family: Arial,Helvetica,sans-serif;"> for constant motion: pull the tape through without changing the speed (either away or towards yourself) <span style="font-family: Arial,Helvetica,sans-serif;"> for no motion: hold the tape, and do not pull or move the tape

Materials: motion detector with USB plug, computer, stiff object

<span style="font-family: 'Times New Roman',Times,serif;">Data Collections: <span style="font-family: 'Times New Roman',Times,serif;">a) Plug the motion detector into the USB port of the computer. <span style="font-family: 'Times New Roman',Times,serif;">b) Materials you will need are as follows: laptop, motion detector, USB link c) 1.<span style="font-family: 'Times New Roman',Times,serif;"> Open the Data Studio program on your laptop. <span style="font-family: 'Times New Roman',Times,serif;">2. Set the motion detector in front of an open space, where objects will not confuse the detector’s motion sensors. <span style="font-family: 'Times New Roman',Times,serif;">3. Hold a stiff object in front of you for the detector to focus on. <span style="font-family: 'Times New Roman',Times,serif;">4. For different demonstrations <span style="font-family: 'Times New Roman',Times,serif;"> To show constant speed, move towards or away from the detector at the same speed. <span style="font-family: 'Times New Roman',Times,serif;"> To show increasing speed, move towards or away from the detector, while increasing your speed. As time passes on the graph, increase the pace to demonstrate acceleration. <span style="font-family: 'Times New Roman',Times,serif;"> To show decreasing speed, move towards or away from the detector, while decreasing speed. As time passes on the graph, increase the pace to demonstrate acceleration.

<span style="font-family: 'Times New Roman',Times,serif;"> Note : Moving towards or away from the detector will determine whether the position-time graph will have a positive or negative slope. The sensor will record the distance of the object from the device at constant intervals of time.

<span style="font-family: Arial,Helvetica,sans-serif;"> The vt graphs are not very good... I think that the scale is too fine and that's why, but still, difficult to see trends this way.
 * <span style="font-family: Arial,Helvetica,sans-serif;">DATA TABLE: **
 * <span style="font-family: Arial,Helvetica,sans-serif;">ANALYSIS AND INTERPRETATIONS: **


 * 1) How can you tell that there is no motion on a…
 * 2) Motion diagram
 * 3) there is no motion on a motion diagram, both velocity and acceleration equal 0. The graph is a single dot.
 * 4) Ticker tape diagram
 * 5) When there is no motion on a ticker tape diagram, the spark will continue to mark the same spot. No motion is represented by the single large dot that will be made on the ticker tape when the tape is not moved.
 * 6) Position vs. time graph
 * 7) When there is no motion on a position vs. time graph, the graph will be a single horizontal line. Where the horizontal line is on the graph depends upon the position.
 * 8) Velocity vs. time graph
 * 9) When there is no motion on a velocity v. time graph, the graph is a single horizontal line. This line is on the x-axis because time (x) increases but y (velocity) does not change. There is no slope because there is no velocity.
 * 10) Acceleration vs. time graph
 * 11) When there is no motion on an acceleration v. time graph, the graph is also a single horizontal line. The line is also on the x-axis because time (x) increases but there is no change in y because there is no acceleration. There is no slope because there is no acceleration. How can you tell that your motion is steady on a…

2. How can you tell that your motion is steady on a...
 * 1) When your motion is steady on a motion diagram, the arrows for velocity are all equal but there is no acceleration. A equaling zero shows constant motion without a changing speed.
 * 2) Ticker tape diagram
 * 3) When your motion is steady on a ticker tape diagram, the dots on the tape are all equally spaced, showing the constant speed.
 * 4) Position vs. time graph
 * 5) When motion is steady on a position vs. time graph, the slope will be equal throughout the whole graph. The slope is positive when the position is getting further and negative when position is getting closer to 0.
 * 6) Velocity vs. time graph
 * 7) When motion is steady on a velocity vs. time graph, the graph will be a horizontal line. Because there is a constant speed, the velocity is not increasing or decreasing and therefore there is no slope to this line. It is on the x-axis because time is increasing but velocity is not changing.
 * 8) Acceleration vs. time graph
 * 9) When motion is steady on an acceleration vs. time graph, the graph is also a horizontal line. There is a constant speed and so once again no slope to this line. Time is increasing but there is no acceleration (slope), showing the constant speed.

3. How can you tell that your motion is fast vs. slow on a…


 * 1) **Motion diagram:** On a motion diagram, the larger the space between the arrows, the slower the object is moving, while the smaller the space between the arrows, the faster the object is moving.
 * 2) **Ticker tape diagram** : On a ticker tape, as the dots gets farther apart, the object is increasing in motion, and if the objects get closer together, the object is decreasing in motion.
 * 3) **Position vs. time graph** : On a position vs. time graph, an object that is going faster, with a larger velocity, has a larger slope, while an object that is going more slowly will have smaller slope.
 * 4) **Velocity vs. time graph** : On a velocity vs. time graph, if the line on the graph is approaching the x-axis, then it is slowing down. If a line is moving further away from the x-axis, it is moving faster.
 * 5) **Acceleration vs. time graph:** If the object is going faster, the line will be above the x-axis, while if it is going slower it will be below the x- axis. X

4. How can you tell that you changed direction on a…
 * 1) **Motion** **diagram** : Seen on motion diagrams is an arrow that is either pointing towards the left or the right, showing a change in direction, an increase or decrease, of the object.
 * 2) **Ticker tape diagram** : On the ticker tape machine, the tape can only be put through the machine from one side, so you are unable to see a change in direction.
 * 3) **Position vs. time graph:** On the position vs. time graph, the change in direction can be seen without the slope. If the slope becomes negative on the graph, the object was moving away from the motion censor, while if it was positive, the object was moving closer towards the detector.
 * 4) **Velocity vs. time graph:** On a v-t graph, the change in direction is seen in relation to the x- axis. If the line is seen above the x-axis, then the line is in the positive region of the graph, while if it is below the x-axis, it is within the negative region.
 * 5) **Acceleration vs. time graph:** On acceleration vs. time graph, you can see if the object changed direction by looking at the line in relation to the y- axis. The higher the line reaches on the y- axis, the further away you are from the  censor, while the lower it is in relation to the y- axis, the closer you are to the censor. X

<span style="font-family: 'Times New Roman',Times,serif;">5. How can you tell that your motion is increasing on a… <span style="font-family: 'Times New Roman',Times,serif;"> a. Motion diagram : On a motion diagram, increasing the size or magnitude of the velocity arrow will show increasing velocity. <span style="font-family: 'Times New Roman',Times,serif;"> b. Ticker tape diagram: As motion increases on a ticker diagram, the dots will appear farther apart. The distance between each set of dots will increase. The ticker tape timer will mark the paper at constant intervals. There will be greater distances between the dots as the ticker tape passes through the machine in between each of the intervals. <span style="font-family: 'Times New Roman',Times,serif;"> c. Position vs. time graph: As motion increases, the slope of the graph will become steeper. If the motion is towards the sensor, the graph will be negative and increasingly steep. If the motion is away from the center, the graph will be positive, and increasingly steep. <span style="font-family: 'Times New Roman',Times,serif;"> d. Velocity vs. time graph: As motion increases, the velocity increases. The y values of the graph should increase, as the x vale (time), increases. <span style="font-family: 'Times New Roman',Times,serif;"> e. Acceleration vs. time graph: To increase motion is to accelerate. Like the velocity-time graph, the y values of the acceleration-time graph will increases. X

<span style="font-family: 'Times New Roman',Times,serif;"> 6. How can you tell that your motion is decreasing on a… <span style="font-family: 'Times New Roman',Times,serif;"> a. Motion diagram: On a motion diagram, the size of the velocity arrow will become smaller and smaller. <span style="font-family: 'Times New Roman',Times,serif;"> b. Ticker tape diagram: The distance between each set of dots on the ticker tape will diminish. While the ticker tape timer will mark dots at constant time intervals, the speed of the paper passing through will decrease. <span style="font-family: 'Times New Roman',Times,serif;"> c. Position vs. time graph: The slope of the graph will decrease. If motion is towards the sensor, then the slope will be negative. If the motion is away form the sensor, then the slope will be positive. <span style="font-family: 'Times New Roman',Times,serif;"> d. Velocity vs. time graph: The velocity decreases in this case. Therefore, the y values will decrease. <span style="font-family: 'Times New Roman',Times,serif;"> e. Acceleration vs. time graph: Because the velocity is becoming slower, then the acceleration is negative, and the y value will decrease as time passes.


 * DISCUSSION QUESTIONS:**

Missing accel vs time 2. What are the disadvantages of representing motion using a...
 * 1) What are the advantages of representing motion using a…
 * 2) Motion diagram
 * 3) An advantage of a motion diagram is that it shows an object's position, velocity, and acceleration at many points of a run. You can see for how long and at what speed the object traveled by the size of the arrows and see what direction the object traveled in as well.
 * 4) Ticker tape diagram
 * 5) An advantage of using a ticker tape diagram is that it clearly shows the speed that the object traveled at. It is an easy diagram to read based on the spacing of dots. They are the only part of the diagram so it is easy to read and simple to analyze.
 * 6) Position vs. time graph
 * 7) An advantage of a position vs. time diagram is that it is one of only two graphs that shows position based on where the object started. When the object gets further away from its starting point, the slope increases, and when the object gets closer to the origin, the slope decreases back towards zero. It is advantageous to use a position vs. time graph if you need to know the objects distance from a certain point.
 * 8) Velocity vs. time graph
 * 9) An advantage of using a velocity vs. time graph is that it is an easy way to see the change in speed. Because the graph shows change in velocity over time (the slope), you may also have the acceleration if there is a positive slope because acceleration is increase in speed.


 * 1) **Motion diagram:** Motion diagrams simply show images of the direction and speed of an object. The disadvantage of these diagrams is that they are unable to portray the numerical values of these different measures.
 * 2) **Ticker tape diagram** : The disadvantage seen within using the ticker tape diagram is that you cannot seen the movement of the tape moving toward the ticker tape machine. For example, you cannot tell the difference between the ticker tape of the tape having an increasing speed away from the ticker tape vs. toward it. It is also disadvantageous due to the fact that on the decreasing motion measures where the dots are extremely close together, they tend to smudge and come too close together to be legible.
 * 3) **Position vs. time graph:** On the position vs. time graph, while the object moves closer to the sensor, there could be a disturbance that will disrupt the accurate lines of the graph. A person could walk by or a chair could be in the way and easily interfere with the position of the actual object moving towards or away from the censor.
 * 4) **Velocity vs. time graph:** On the velocity vs. time graph, when you lifted your leg to walk or moved your hand, the censor picked up these small, gentle movements, and would look extremely abrupt on the graph. This shows how the graph was not always perfectly accurate and easily influenced by outside interferences.
 * 5) **Acceleration vs. time graph:** On the acceleration vs. time graph, it shows the rate of the change of velocity, yet if the velocity were not completely accurate, this would not be accurate either.
 * 1) **Acceleration vs. time graph:** On the acceleration vs. time graph, it shows the rate of the change of velocity, yet if the velocity were not completely accurate, this would not be accurate either.

<span style="font-family: 'Times New Roman',Times,serif;">3. Define the following: <span style="font-family: 'Times New Roman',Times,serif; margin-bottom: 0.0001pt; margin-left: 1in; text-indent: -0.25in;">1. No motion: No motion means that the object has no velocity, acceleration. The object is still without any change in position. <span style="font-family: 'Times New Roman',Times,serif; margin-bottom: 0.0001pt; margin-left: 1in; text-indent: -0.25in;"> 2. Constant speed: Constant speed refers to a constant velocity. At constant velocity, there is no change in the rate of motion for the object- no acceleration. <span style="font-family: 'Times New Roman',Times,serif; margin-bottom: 0.0001pt; margin-left: 1in; text-indent: -0.25in;"> 3. Increasing speed: At increasing speed, an object accelerates in the direction of its velocity to increase its velocity. 4. Decreasing speed: At decreasing speed, an object accelerates in the opposite direction of its velocity. This decreases the object’s velocity.


 * CONCLUSION:**

** Results: **

The results of these experiments show that our hypotheses were correct. The ticker tape diagram represented velocity and acceleration. When the tape was pulled slowly, the dots were very close together. However, when the tape was pulled quickly the dots were far apart. The faster the speed, the further apart the dots were, showing the far distance that the tape moved in a small amount of time. The ticker tape diagrams did not look any different when pulled in a different direction. These diagrams represented speed and change in speed, but not change in position. On a position vs. time graph, the slope increased when we moved away from the motion detector. The slope decreased and came back towards zero when we moved closer to the starting position. The graph demonstrated our distance and also the direction we were moving in relation to the starting point. On a velocity vs. time graph, the slope, or change in speed/change in time, is the acceleration. When there was velocity moving in a positive direction, the line of the graph is in the positive quadrants. The graph is seen as speeding up when the line is getting further away from the starting point, either in the positive or negative quadrants. When the line is in the negative quadrant it just means the speed is increasing but away in the negative direction. You can solve acceleration by finding the slope of two points on a velocity vs. time graph. On the acceleration vs. time graphs, the slope increases as acceleration increases. The slope decreases when the object is decelerating. The acceleration vs. time graphs are similar to the velocity vs. time graphs because they show the change in speeds over time


 * Errors:** There could have been many possible errors seen within the lab. First and most obvious of all, when using the motion censor, any outside interference could have affected the accuracy of the final graphs. If there was an object in the way or a hand swung on the side of ones body as they walked, then the graph's outcome would not have been completely correct. With the graphs as well, if we were supposed to be walking at a constant speed in front of the motion censor, one of us could have started to walk a tad faster or slower, which would have drastically change the results. This was seen on the ticker tape as well. While pulling the tape out of the machine, errors could have been made if the tape was pulled out too fast or too slow while trying to have constant motion. Otherwise, the graphs/ ticker tapes were accurate to the best of our abilities, and portrayed the different aspects of motion in the most correct form possible.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 10pt;">Implications: The Ticker Tape Experiment demonstrates that the ticker tape is not a good device if one needs to determine direction, one of the main components of vectors, such as velocity. The ticker tape timer is better suited for measuring changes in speed, rather than velocity. The motion sensor, on the other hand, well demonstrates how motion involves the combined relations of displacement, velocity, and acceleration. As position changes, velocity will change. If the position begins to change more quickly, and the object is moving greater distances at a faster pace, then the velocity of the object is increasing. Changes in velocity appear in the acceleration graph, because acceleration is the change in velocity. As the velocity increases, the acceleration increases. In the same way, as the velocity decreases, acceleration also decreases. When an object does not change position, then the velocity is reflected as zero, which will lead to an acceleration of zero. Read description. This is all true but isn't what I'm looking for.