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Group: Andrew Miller, Navin Raj, Ryan Listro

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//A Crash Course in Velocity//, 9/20/10, Navin Raj, Ryan Listro, Andrew Miller Purpose Hypothesis: Given the position graph, we are able to find the velocity graph by looking at its slope. The velocity graph will be steeper than the position graph. Procedure:
 * 1) Tape 1 battery car to spark timer.
 * 2) Turn spark timer on (make sure car isn’t in front of any objects for optimal test results).
 * 3) Labeled 25 points on the spark timer in intervals of 1/10 of a second (starting with 0).
 * 4) Measure from the 0 to the closest point (.1), then to the next point (.2) and so on.
 * 5) Plug data into excel spreadsheet with columns titled seconds, 1-battery truck, and 2-battery truck.
 * 6) Make a graph of data of truck with one battery, truck with two batteries, and together.
 * 7) For problem a, find out where the two vehicles will intersect experimentally by spacing the two vehicles apart by 600 cm.
 * 8) Start the two vehicles at the same time and let them go.
 * 9) Do this five times, and then average the results.
 * 10) For problem b, set the faster vehicle one meter behind the slower vehicle, and then let the faster vehicle catch up to the slower one.
 * 11) Do this five times, and then average the results.
 * 12) Find the percent error of the trials, and then average.

Materials: 2 constant motion vehicles (Slow 3, Fast 3), tape, meter stick, masking tape (about 30 cm), stopwatch, spark timer, spark tape, and Microsoft Excel

Observations:

Data (excel spreadsheet, table of trials) better to do screenshot of just the graph, instead of the entire screen (shift-command-4) graph goes after data.

these headings are incorrect...
 * Distance from 0 (cm) || 1 Battery truck (cm) || 2 Batteries truck (cm) ||
 * 0 || 0 || 0 ||
 * 0.1 || 1.40 || 3.30 ||
 * 0.2 || 2.40 || 6.40 ||
 * 0.3 || 3.40 || 9.90 ||
 * 0.4 || 4.60 || 13.30 ||
 * 0.5 || 5.60 || 16.90 ||
 * 0.6 || 7.10 || 20.20 ||
 * 0.7 || 8.30 || 24.00 ||
 * 0.8 || 9.50 || 27.40 ||
 * 0.9 || 10.50 || 31.10 ||
 * 1.0 || 11.70 || 34.60 ||
 * 1.1 || 13.00 || 37.90 ||
 * 1.2 || 14.00 || 40.70 ||
 * 1.3 || 15.00 || 45.60 ||
 * 1.4 || 16.20 || 49.10 ||
 * 1.5 || 17.50 || 52.60 ||
 * 1.6 || 18.50 || 56.30 ||
 * 1.7 || 19.80 || 59.90 ||
 * 1.8 || 20.90 || 63.50 ||
 * 1.9 || 22.10 || 66.90 ||
 * 2.0 || 23.30 || 70.70 ||
 * 2.1 || 24.50 || 74.20 ||
 * 2.2 || 25.50 || 77.80 ||
 * 2.3 || 26.90 || 81.40 ||
 * 2.4 || 28.10 || 85.60 ||
 * 2.5 || 29.40 || 88.70 ||



(Note: Catching Up and Crashing Positions are from the perspective of the slower car).
 * Trial # || Catching Up Position (cm) || Crashing Position (cm) ||
 * 1 || 150 || 190 ||
 * 2 || 154 || 189 ||
 * 3 || 155 || 185 ||
 * 4 || 152 || 180 ||
 * 5 || 154 || 187 ||
 * Average: || 153 || 186 ||

//Calculations://



very well organized, easy to follow! great results



//Here is our copy of all the math.// ?

//**Discussion Questions:**//

1. Why is the slope of the position-time graph equivalent to average velocity? //The equation for slope is (y1-y2)/(x1-x2). In our graph, the y-values represent position and the x-values represent time. Basically, the slope in our graph equals position (or distance) over time. Distance over time is also the equation for average velocity.//

2. Why was it okay to set the y-intercept equal to zero? //The y-intercept is equal to zero because of 2 reasons. One reason is that there can not be a negative position/ distance in this instance. Another reason is that the position cannot change if time does not increase. For example, before starting the spark timer (at 0 s), there isn't and can't be a change in distance. Therefore, the y-intercept is equal to zero.//

3. What is the meaning of the R^2 value?

//The R^2 value is an indication of how well one's results fit onto the line of best fit. In other words, it is an indication of how precise one was in his or her measurements (in this case, these measurements were the distance between each of the points on the ticker tape diagram.//

4. Where would the cars meet if their speeds were exactly equal?

//If the two speeds were exactly equal, then the cars would meet at the midpoint of the distance that they have to travel (for example, if the distance is 600 cm, the two cars would meet at the 300 cm mark.//

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.




 * The above graph shows the amount of time it took for the cars to crash into eachother over a certain position. They met at exactly 113.79cm after 9.7554s.**




 * The above graph shows the amount of time it took for the cars to catch up to one another over a certain position. They met at exactly 150cm after 4.25s.**

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?//



Fantastic!
 * It is not possible to find an exact point where these two trucks meet on this graph because the positions are not listed. The velocity lists the speed at different positions over time. Since the trucks were both at constant speed at every position, there is no change in the individual lines. Thus, no point of intersection listed in the velocity.**

missing conclusion!



=**Comparing Qualitative Representations of Motion 9/13/10**= Purpose? Procedure: 1. Set up motion sensor via USB in front of flat surface (e.g.- wall). 2. Using data studio, measure distance, velocity, and acceleration in the following conditions: a. No motion- stand about a meter away- do not move. b. Increasing speed towards the sensor- move to the sensor, gradually increasing your speed. c. Increasing speed away from the sensor- move away from sensor, gradually increasing speed. d. Constant speed towards the sensor- maintain same speed towards the sensor. e. Constant speed away from the sensor- maintain same speed away from sensor. f. Decreasing speed towards the sensor- move towards the sensor, starting quickly, but gradually decreasing speed g. Decreasing speed away from the center- move away from the sensor, starting quickly but gradually decreasing speed. 4. Place data (graphs) into a table by drawing or taking a screen shot. 5. Using a spark timer and ticker tape, slide the ticker tape into the machine, and measure the following: a. No motion b. Increasing speed away from spark time- place tape into spark timer, and pull it out, gradually increasing the speed at which you pull it out. c. Constant speed away from spark time- place tape into spark timer, and pull it out, maintaining same speed. d. Decreasing speed away from spark timer- place tape into spark timer and pull it out, starting quickly but gradually reducing speed. Motion diagrams?

Analysis and Data Interpretation:

1. a. No motion is indicated by a sole dot- the acceleration and velocity are both 0. b. There are just two dots that looks like a colon, which could have only happened if the tape had stayed in place. Over time, the dots would get thicker because the spark timer would make more and more dots on the same spots. c. The graph is constant at the distance that the sensor is from the wall, meaning that the graph looks like a horizontal line. d. The graph is constant at 0, meaning that there is no change in speed of the object. e. Theoretically, the graph should be constant at 0 because acceleration is a measure of the change of slope in velocity and in this case, the velocity is 0. Though our graph is not at 0, it does vacillate around 0.

2. a. The arrows are facing the same direction and are of equal length- the acceleration is 0 and the velocity is constant. b. The colons on the ticker tape are evenly spaced from each other. c. In this graph, motion is steady when one covers the same distance in the same time, meaning that the slope remains the same. d. Your velocity is constant at a certain speed- if one is going toward the sensor, then velocity is negative; if one is going away from the sensor, then velocity is positive. e. With acceleration, one can tell that there is neither motion nor constant motion, for acceleration is a measure of the slope of velocity; however, velocity has a slope of 0 during both no motion and constant motion; therefore, just looking at the acceleration graph does not give a good indication of the slope, direction, or speed at which a person or object is traveling.

3. How can you tell your motion is fast vs. slow on a... V V V V -> --> > --> a= > Slow motion would be represented by lines that start large and end small, and an acceleration in the opposite direction of the velocity. V V V V V V > --> > ---> --> -> a=<
 * a.** Fast motion on a motion diagram would be represented by increasingly long lines and an acceleration in the same direction as the increase.
 * b.** Motion, whether fast or slow, is shown by the small, round, black sparks created by the ticker. If the motion is fast, then the ticker will have very few dots spread out over the surface of the tape. This is because the ticker does not have enough time to make contact with the tape at a fast pace. On the other hand, slow motion can be identified by numerous, closely confined black sparks on the tape that occur at random intervals. This is because the ticker has much more time to make contact with the slow moving tape.
 * c.** You can tell fast motion on a position vs. time graph because the time it takes to get from one position to another is much less than if you are in slow motion. Slow motion will need an increased amount of time to reach the same point that the fast motion ended at. In the fast motion graph, the line will be much steeper than in the slow motion. It would be at the target point over a shorter amount of time.
 * d.** Fast motion, in the velocity vs. time graph, will be represented as a shorter line than slow motion graphs of velocity vs. time. This is because is you move at fast motion; the velocity, which is speed in a given direction, will be shorter because of the faster speed you are moving at.
 * e.** Slow motion, in the acceleration vs. time graph, would not differ from fast motion because the change in speed that leads up to the constant would be the same whether you decrease or increase.

4. How can you tell that you changed direction on a... V V V V V <- <--- <- <--- <-
 * a.** Changes in direction on a motion diagram can be identified by which way the lines move. For example, if the direction is shown as increasing towards, the diagram would look like:

The lines would be coming into the left if your are moving towards, whereas if it were increasing away, the lines would increase in size to the right. By seeing whether the lines move to the right or left, you can tell the general direction that the line is moving in.
 * b.** A ticker tape diagram can only go away from oneself, it is not possible to show another direction in the test we performed. Thus, you would not be able to tell direction of motion, only the speed at which it happened.
 * c.** We tested from two positions, going towards and away from our sensor. In order to tell if you changed direction on a position vs. time graph, you would have to observe whether the amount of distance covered increases or decreases. If it increases, then you know that you changed direction going away from the sensor. However, if it decreases, then you know you changed your direction towards the sensor.
 * d.** Once again testing with the two positions, it can be seen that the velocity vs. time graph will either increase in velocity or decrease in velocity depending on your position. One can tell your direction is away if the graph beings to increase in velocity, the opposite is true if you are towards the sensor. This is because as you get closer, there is less room for the sensor to travel and the waves become decreased.
 * e.** The acceleration vs. time graph tells you that direction has changed by increasing the acceleration if you are away, and decreasing the acceleration if you are positioned towards the sensor. This is due to the change in velocity, as you come closer, decreases over time.

5. a. Motion is increasing on a motion diagram when the arrows start out shorter and become longer after each previous arrow. For increasing speed toward, the arrows would be facing right to show the direction of the motion. The direction of the arrows for the increasing speed away would be vice vera. The pattern for increasing speed away would look similar to the one below (opposite direction for speed toward): ->-->--->>--->---> b. The spark timer makes a mark on the tape that looks like a colon. As the tape is fed through the machine with increasing speed, the colon-looking marks become more and more spread apart. Basically, you can tell that the motion is increasing if the marks from the spark timer look somewhat like the pattern below:

c. Motion is increasing on a position vs. time graph when the slope of said graph is curved rather then being completely flat and straight like that of a constant motion graph. For increasing speed toward, the x values increase while the y values decrease. For increasing speed away, both the x and y values increase. d. You can tell there is increasing motion on a velocity vs. time graph when the slope of the line on the graph is slanted. The slanted line also has to start at the origin **__and__** have increasing x values. For increasing speed toward, there has to be a negative slope and vice versa for increasing speed away. e. Motion is increasing on an acceleration vs. time graph when the line has a 0 slope and is either below or above the x-axis. For increasing speed toward, the line has to be below the x-axis and vice versa for increasing speed away.

6. a. Motion is decreasing on a motion diagram when the arrows start out longer and become smaller after each previous arrow. For decreasing speed towards, the arrows would be pointing the the left, and vice versa for decreasing speed away. The pattern for decreasing speed toward would look similar to the one below (opposite direction for speed away): <-<---<<<---<- b. Motion is decreasing on a ticker tape diagram when the marks made by the spark timer start out spaced out and become closer and closer. You can tell the motion is decreasing when the marks look like the pattern below:
 * uhsdufohosduhfo : hidbfidsbidbdu : djhdjdjdjdjdjd : dhjdjdjdjd : dhjdhdhd : dhdhdh : dhdhd : dhd : dh ::

c. Motion is decreasing on a position vs. time graph when the line of said graph is curved. For decreasing speed towards, the x values have to increase and the y values have to decrease. For decreasing speed away, the x and y values have to both be increasing from the origin. d. Motion is decreasing on a velocity vs. time graph when the line of said graph is slanted. For decreasing speed towards, both the x and y values are increasing from the negative part of the y-axis. For decreasing speed away, the x values increase while the y values decrease from the positive part of the y-axis. e. Motion is decreasing on an acceleration vs. time graph when the line of said graph has a slope of 0 and is either above or below the x-axis. For decreasing speed towards, the line is above the x-axis and vice versa for decreasing speed away.

Discussion Questions:

1. a. Using a motion diagram is good for linear motion, meaning up, down, left, or right. Towards and away are easily indicated by going right and left respectively. Motion diagrams are good for simplicity. b. The ticker tape diagram is very simple to read and easy to understand (if the colons are farther apart, then the speed of the tape is greater). c. Visually, a position vs. time graph is very easy to depict a person's location and how long it takes that person to reach another location and how far that person had to travel. d. The velocity vs. time graph is a good representation of motion because it allows you to see if the velocity is positive or negative. With that, one can see where a person came from--if velocity is positive, then the person is going away from an object; if velocity is negative, then the person is going towards an object. e. Acceleration measures the rate of change in velocity. The acceleration can give basic information about velocity (whether the velocity is changing in a positive or negative direction).

2. What are the disadvantages of representing motion using a...
 * a.** Motion diagrams can do not give any numerical measurements, you can only tell whether something is increasing, decreasing, not moving, at constant speed, or going in different directions. They are simple, but cannot be used for calculation.
 * b.** The ticker tape diagram is a great tool to show the basic changes between moving fast and slow. However, one disadvantage is that it can be inaccurate if you do not constantly keep increasing or decreasing your speed. The tape will be smeared, and marks that should be spread apart, might be close together if your speed was not maintained. Also, the ticker tape only goes in one direction, so your position is limited to moving away or staying still.
 * c.** By using a position vs. time graph, you are relegated to only visually seeing that one movement is faster than another. There can be no comparisons of exact speeds, only approximations made from the amount of time it took to cover a distance. Distance can also be hindered by obstructions such as uneven ground, or not constantly increasing, decreasing, or maintaining speed. Also, distance can change depending on where you stand. Unless you measure from exactly the same position every time, the representation of motion will be different and inaccurate.
 * d.** The disadvantages to representing motion through a velocity vs. time graph is that speed can be affected by obstructions like uneven ground. This would lead to sudden drops or spurs in the speed, and corrupt results.
 * e.** By representing motion through the acceleration vs. time graph, you are assuming that the velocity changed enough to show motion. If there was only a very infinitesimal change in velocity, then it would be difficult to represent the acceleration change. The motion would seem non-existent.

3. a. No motion is when either there is no object or person moving in the view of the motion detector (also when the tape is not moving through the spark timer. While there is no motion, the graphs appear as such: a colon-shaped object on the ticker tape diagram, a horizontal line on the position vs. time graph that is directly proportional to the closest steady object in the sight of the motion detector, and a horizontal line with x values of zero on the velocity vs. time and acceleration vs. time graphs. b. Constant speed can be defined by an object moving at the same speed and never increasing or decreasing in velocity or acceleration. The only variable that does, in fact, change is the position, which can increase or decrease depending on the direction of the motion. c. There is an increase in speed when an object or person, in the view of the motion detector, moves at one speeds and starts to more faster as time elapses. As a result, both the acceleration and velocity increase.

=
d. There is a decrease in speed when an object or person, in the sight of the motion detector, moves at one speed and starts to slow down as time passes. As a result of the motion, both the acceleration and velocity will decrease, and the distance will change depending on the direction of the motion.======

Conclusion:

In this lab, we investigated the different qualitative ways to represent motion, including using a ticker tape diagram, distance, velocity, and acceleration as a function of time. In our findings, we discovered how changing a person’s speed (or leaving it constant) and direction affect his distance from an object and his velocity and acceleration as he is approaching or moving away from that object. In order to test this, we took a human subject and had him increase, decrease, and keep his speed constant as he moved towards and away from the sensor. From this, we discovered how time affects distance, velocity, and acceleration. In terms of applications outside of physics, we discovered that these three concepts are used in calculus, specifically using the derivative, which is simply the slope of the tangent line to a function. When one takes the derivative of the position graph, one attains a graph for the velocity. Taking the derivative of the distance (position) graph gives one the velocity graph; taking the derivative of the velocity graph gives one the acceleration graph. Using these principles, we can predict what the velocity and acceleration graphs would look like. For example, if the subject is moving towards the sensor, we know that the distance is decreasing; therefore, velocity (the slope of the distance graph) is negative. If the velocity graph had a constant slope at y = 0, then we know that because the acceleration graph is the slope of the tangent line to the velocity graph, the slope of the acceleration graph is 0; therefore, the acceleration graph is a horizontal line on y = 0. Error in our graphs could have occurred if the sensor had picked up on the subject’s legs, which is why he put a folder in front of his abdomen. Besides machine error, human error could have occurred as well—perhaps the test subject decreased his speed when moving towards the sensor instead of keeping constant. If that had happened, we would see a slight change in the slope of the distance graph, and a decrease in velocity and acceleration. good. how would you address these errors to get rid of them?