Ch2_SmithJ

= = toc 1-D Kinematics

Class Notes (9/6/11)

 * distance - how far; not relative to starting place
 * position - where you're located, relative to a known location
 * displacement - requires direction, how far in that direction, relative to your starting point
 * speed and velcoity are often used as synonyms
 * speed - the rate of change of your position; how fast
 * velocity - total displacement
 * to measure speed, you need time and distance
 * reaction time - 10th of a second so it can be a flaw in measurements like a stop watch
 * hertz - measure of frequency
 * V = total distance/ total time
 * the smaller the distance, the more precise

Lesson 1:

 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * I understood the difference between distance and displacement well from our classroom discussion. The distance is a scalar quantity, which means that it is numerical. Distance is adding up the entire amount traveled, opposed to displacement. Displacement is a vector quantity and is calculating how far something is from the starting point, regardless of how it got there.
 * In this image, the total distance traveled from 0 minutes to 3 minutes is 420 m because it is a cumulative amount of where the skier has been since he started, but the skier only displaced 140 m because at the 3rd minute he is only 140 m from where he was at 0 minutes.
 * I understood the difference between instantaneous speed and average speed. Instantaneous speed is the rate at a given point in time. It can be taken for any time, and if the object is moving at a constant rate the instantaneous speed should be the same at all times because the speed is never changing. Average speed is the average of the speeds at all times, meaning the average of the instantaneous speeds. This is because if an object is not moving at a constant rate, the speed will be changing depending on the point in time. The average speed will tell what speed the object was moving through out the time of its travel.
 * 1) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
 * I was confused about the difference between speed and velocity. I was thinking that they were the same, but now I understand that speed and velocity are different. Speed is the rate that an object is covering ground in. In other words, it is how fast or slow an object covers a certain distance. Speed is also a scalar quantity which means that direction doesn't matter. Contrasting, velocity is a vector quantity which means that direction does matter. Velocity relates more to the final position than the path taken to get to that position.
 * 1) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * Are velocity and displacement the same because they are both measuring the final position compared to the beginning position?
 * displacement is the net change and velocity is the speed at which you do it
 * 1) What (specifically) did you read that was not gone over during class today?
 * I did not remember discussing the difference between scalars and vectors. After reading, I understand that scalar is a numerical value while vectors are numerical values with a given direction.

Class Notes (9/9/11)

 * Average speed
 * average of the total speed
 * Constant speed
 * ratio of the distance an object is going and the time spent
 * Instantaneous speed
 * speed at a specific time interval
 * if an object is going at constant speed, the instantaneous speed is always the same
 * FORMULA FOR ALL: change in distance/ change in time
 * for instantaneous speed, will be really small
 * Types of Motion
 * at rest
 * standing still in the same place
 * constant speed
 * speed is not changing
 * increasing speed
 * decreasing speed
 * <span style="font-family: Arial,Helvetica,sans-serif;">How can we represent these types of motion?
 * Motion Diagrams
 * show direction of velocity
 * if at rest, v=0 and a=0
 * constant speed --> --> --> ; a=0 because arrows are same length and acceleration is 0
 * increasing --> > > and a is ---> because it is moving forward (positive)
 * decreasing speed --> ---> ---> and a is < because it is negative
 * [[image:Screen_shot_2011-09-09_at_9.29.24_AM.png]]
 * to represent direction, you draw arrows going the direction that the object would be moving
 * throwing something upward has a decreasing speed
 * Ticker Tape Diagram
 * [[image:Screen_shot_2011-09-09_at_9.33.27_AM.png]]
 * if at rest, the ticker tape would just have one dot
 * if decreasing, the dot would be getting closer together at the end
 * negatives of ticker tape diagrams:
 * cant tell direction
 * positives:
 * you can find an exact value and measurements
 * <span style="font-family: Arial,Helvetica,sans-serif;">acceleration
 * changing speed
 * can be slowing down or speeding up
 * <span style="font-family: Arial,Helvetica,sans-serif;">Signs
 * arbitrary and subjective
 * up and right = positive
 * left and down= negative
 * <span style="font-family: Arial,Helvetica,sans-serif;">Kinematics
 * study of motion

<span style="color: #2db33f; font-family: Arial,Helvetica,sans-serif;">Lesson 2:

 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * From our class discussion, I understood both ticker tape diagrams and vector diagrams. Ticker tape diagrams help to show the velocity of an object but it does not show direction. Ticker tape diagrams work by having ticker tape attached to an object threaded through a small machine that marks specific time intervals. If the dots on the tape are very close together it means that the object was moving slowly because it covered less distance in a time interval, opposed to dots that were very spread out because the object was covering more distance. If an object is stopped the ticker tape diagram will have a single blotched dot. If the object is accelerating, the dots will either be going from more spread to closer (negative) or from closer to more spread (positive). Ticker tape diagrams are also helpful because it allows for exact measurements.
 * Vector diagrams show the direction and acceleration of an object. They show direction by using a series of arrows and acceleration with arrows as well but they are not exact as ticker tape diagrams are. For an object moving at constant speed forward, the vector diagram will show the same sized arrows for v and a will equal 0 because there is no change in speed. If the object is decreasing speed the a is going to be facing backward and the velocity arrows are going to be going from longer to shorter. If it is increasing speed the arrows will be going from smaller to larger with an acceleration arrow going forward.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">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.
 * After class, I was still a little bit shaky on the different ways a ticker tape diagram could look. By reading the Physics Classroom section, I feel that I have a better understanding on the different formation of dots that can be shown in a ticker tape diagram such as being stopped.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * I understood everything in this section.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that was not gone over during class today?
 * In class, we discussed both vector diagrams and ticker tape diagrams.

<span style="color: #234bbd; font-family: Arial,Helvetica,sans-serif;">Class Notes (9/13/11)
<span style="color: #234bbd; font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">acceleration- rate that velocity is changing (a) (m/s^2)

<span style="font-family: Arial,Helvetica,sans-serif;">a= (v final-v initial)/ time --> V final = V initial + a*t (doesnt have displacement)

<span style="font-family: Arial,Helvetica,sans-serif;">V= d/t ONLY for average or constant speeds <span style="font-family: Arial,Helvetica,sans-serif;">V= (v1+v2) / 2 only for average speed

<span style="font-family: Arial,Helvetica,sans-serif;">1/2(V initial + V final) = (displacement/time) <span style="font-family: Arial,Helvetica,sans-serif;">displacement= 1/2 (v initial + v final) t (Doesnt have acceleration) <span style="font-family: Arial,Helvetica,sans-serif;">displacement= V initial * t + 1/2 a*t^2 (doesnt have V final) <span style="font-family: Arial,Helvetica,sans-serif;">V final ^2= V initial ^2 + 2ad (doesnt have t)

<span style="color: #2db33f; font-family: Arial,Helvetica,sans-serif;">Lesson 1e:
<span style="font-family: Arial,Helvetica,sans-serif;">After reading the material, answer the following questions:
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * I already understood that acceleration is different than "sports announcers" describe it as. In class we discussed that acceleration is just the change in velocity. A person could be moving extremely slow, but if their velocity is going up, they are accelerating. Similarly, if a person is slowing down, that is also considered an acceleration because there is a change in velocity.
 * I also understood that constant velocity and constant acceleration are different. Constant velocity should have no acceleration because it is constantly going the same rate, so there is no change in the velocity, or acceleration. Constant acceleration is when an objects velocity is continuously going up be an interval. The reading used the example of an acceleration increasing by 5 m/s constantly, which would be constant acceleration.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">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.
 * After class I was still a little bit shaky on the idea that positive acceleration is moving forward and negative acceleration is slowing down. I feel that the animation and wording of the reading helped me to fully understand what a drawing would look like with different velocity. It now makes sense that a positive acceleration is a positive increase in velocity while negative is the opposite.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * I understood everything in the reading.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that was not gone over during class today?
 * I don't believe that we discussed free falling objects. Free falling objects have a velocity that is constantly accelerating. It is not constant acceleration because as the object is falling the velocity is going up from smaller to larger intervals.

<span style="font-family: Arial,Helvetica,sans-serif;"> RULE OF THUMB is: If an object is slowing down, then its acceleration is in the opposite direction of its motion.

<span style="color: #2db33f; font-family: Arial,Helvetica,sans-serif;">Lesson 3:

 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * I previously understood position vs. time graphs. Position time graphs are very helpful in finding velocity. The reading stated, "As the slope goes, so goes the velocity". A position time graph can show constant velocity, which would just be a straight line with a constant slope, or an accelerating velocity which will be like a curve. Velocity on a position time graph can also be positive or negative. Negative velocity is going toward the origin and positive is going away from the origin.
 * I also fully understood how to calculate the slope of a line. It is the different between the y points divided by the difference in the x points.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">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.
 * There was nothing that I was shaky on that the reading helped me understood. I thought that I was confidence coming away from class and am only reassured with my confidence.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * I understood everything in the reading.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that was not gone over during class today?
 * We hadn't discussed what being stopped would look like on the graph. It just looks like a straight line at the origin on the velocity graph but on a position graph it is just a straight line.

<span style="color: #2db33f; font-family: Arial,Helvetica,sans-serif;">Lesson 4:

 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
 * I understood the slopes of velocity time graphs from our class discussion. If the slope is 0 then there is no acceleration because the velocity is not changing, while an object that is accelerating has a slope because the object is increasing in acceleration each point. I also understood that the slope is equal to the acceleration.
 * I also understand what all of the graphs of the different types of velocities look like.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">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.
 * After class I was still a little bit shaky on the idea that an object that is increasing velocity (speeding up) in the negative is moving away the the axis. Because of the negative numbers, I thought that speeding up would be going toward the axis and want to become a smaller negative number but now I understand that it is actually becoming a larger negative number which actually has a larger velocity than a small negative number.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
 * I understood everything in the reading.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What (specifically) did you read that was not gone over during class today?
 * We did not discuss how to find area of a graph. It can be done by creating a shape (square, trapezoid, rectangle) inside of the graph and finding the area of that object.

<span style="color: #2db33f; font-family: Arial,Helvetica,sans-serif;">Lesson 5:
<span style="font-family: Arial,Helvetica,sans-serif;">a. 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: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Ticker Tape Diagram or dot diagram of its motion would depict an acceleration. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. If an object travels downward and speeds up, then its acceleration is downward
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Free-falling objects do not encounter air resistance.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for //back-of-the-envelope// calculations)

<span style="font-family: Arial,Helvetica,sans-serif;"> b. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. This quantity known as the acceleration of gravity has special symbol- the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s/s. There are slight variations in this numerical value that are dependent primarily upon on altitude.

<span style="font-family: Arial,Helvetica,sans-serif;">c. A position versus time graph for a free-falling object is shown below.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">A curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration, it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). The negative slope of the line indicates a negative (i.e., downward) velocity. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">A velocity versus time graph for a free-falling object is shown below.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. The velocity-time graph reveals that the object starts with a zero velocity and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. The constant, negative slope indicates a constant, negative acceleration.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">d. Free-falling objects are in a state of [|acceleration]. The formula for determining the velocity of a falling object after a time of t seconds is <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">** vf = g * t ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">where g is the acceleration of gravity. The value for g on Earth is 9.8 m/s/s. The above equation can be used to calculate the velocity of the object after any given amount of time when dropped from rest. Example calculations for the velocity of a free-falling object after six and eight seconds are shown below. <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">** Example Calculations: ** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">At t = 6 s

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">vf = (9.8 m/s2) * (6 s) = 58.8 m/s <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">At t = 8 s

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">vf = (9.8 m/s2) * (8 s) = 78.4 m/s <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. This distance can be computed by use of a formula; the distance fallen after a time of t seconds is given by the formula. <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">** d = 0.5 * g * t2 ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px;">where g is the acceleration of gravity (9.8 m/s/s on Earth). Example calculations for the distance fallen by a free-falling object after one and two seconds are shown below. <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">** Example Calculations: ** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">At t = 1 s

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">d = (0.5) * (9.8 m/s2) * (1 s)2 = 4.9 m <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">At t = 2 s

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">d = (0.5) * (9.8 m/s2) * (2 s)2 = 19.6 m <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">At t = 5 s

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">d = (0.5) * (9.8 m/s2) * (5 s)2 = 123 m

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 13.3333px; text-align: center;">(rounded from 122.5 m)

<span style="font-family: Arial,Helvetica,sans-serif;">e. The acceleration of gravity is the same for all free-falling objects regardless of how long they have been falling, or whether they were initially dropped from rest or thrown up into the air.  <span style="font-family: Arial,Helvetica,sans-serif;">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: Arial,Helvetica,sans-serif;">The actual explanation of why all objects accelerate at the same rate involves the concepts of force and mass. Increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. Thus, 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="font-family: Arial,Helvetica,sans-serif;">Extra Class Notes:
<span style="font-family: Arial,Helvetica,sans-serif;">Constant Speed Graphs <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;">Interpreting Position Time Graphs <span style="font-family: Arial,Helvetica,sans-serif;">

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

<span style="font-family: Arial,Helvetica,sans-serif;">10/3/11 <span style="font-family: Arial,Helvetica,sans-serif;">**Free Fall**- only gravity is acting on object, no other acceleration forces. IGNORE AIR RESISTANCE!

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

<span style="font-family: Arial,Helvetica,sans-serif;">**CMV Lab (9/8/11)**
<span style="font-family: Arial,Helvetica,sans-serif;">** Objective: ** a.) What is the speed of a Constant Motion Vehicle (CMV)? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">b.) How precisely can distance be measured? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">c.) What does a position-time graph tell you?

<span style="font-family: Arial,Helvetica,sans-serif;">** Hypothesis: ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">a.) A CMV moves 1 ft/s <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">b.) Distance can be measured to the 1000th decimal place using significant figures <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">c.) A position time graph tells you the amount of time traveled from a starting position to the current position

<span style="font-family: Arial,Helvetica,sans-serif;">** Data: ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;"> <span style="font-family: Arial,Helvetica,sans-serif;">** Discussion questions **
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">Why is the slope of the position-time graph equivalent to average velocity?
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px;">The slope is the change in y value over the change in x value. The y-axis was the position, and the x-axis was time. Because the slope ended up being change in distance, or position, over change in time, this is the velocity formula, indicating that the slope is equal to the velocity.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">Why is it average velocity and not instantaneous velocity? What assumptions are we making?
 * 4) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px;">Average velocity is the velocity over time and instantaneous is the velocity at a certain point in time so it would not be helpful in finding the constant speed. We are assuming that the average velocity will be the same as the instantaneous velocity as long as the points are incredibly close together.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">Why was it okay to set the y-intercept equal to zero?
 * 6) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px;">It is okay to set the y-intercept equal to zero because when the y-axis or the position was at 0 the time was also zero, indicating that the coordinates of this point would be (0,0) and the trend line should cross the y-axis at that point.
 * 7) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">What is the meaning of the R2 value?
 * 8) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px;">The R2 value is percentage of points described by the trend line. If the R2 value is closer to one, it means that the results are more likely accurate than if it is farther from one. We chose a linear graph because the R2 value would be closer than an expediential graph.
 * 9) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">If you were to add the graph of another CMV that moved more slowly on the same axes as your current graph, how would you expect it to lie relative to yours?
 * 10) <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px;">The line would be much lower on the graph, and would have more spread out points. Because the points are much lower the velocity/slope would be lower because the CMV would be going slower than my CMV.

<span style="font-family: Arial,Helvetica,sans-serif;">** Conclusion ** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">The yellow CMV that I was given has a velocity of 28.274. The R2 value was .9993, which indicates that there is a 99.93% chance that my results are accurate. My hypothesis for the question of how fast does a CMV move was that the CMV would move 1 ft/s, which was relatively accurate. The actual velocity is 28.274 cm/s and my hypothesis was 30 cm/s, which are reasonably close. The hypothesis I created for the second question about the precision of measuring distance was that it could be measured to the 1000th when it actually is measured to the 100th in this lab. My hypothesis was that a position-time graph tells about the time traveled to a certain point when it actually tells the velocity or speed. It is probable that error could have occurred in many areas of the lab. We had to estimate the hundreds place when measuring the distance of the dots; the estimates could have been off which would create error in the measurements. During this measuring process, it is also possible that the meter stick moved which would throw the results off. Lastly, it is possible that when we measured the dots, we were looking at the meter stick on an angle because of the way we were sitting, which may have made the measurements look different than they actually were. If this lab was redone, using a flatter measuring tool could have minimized error. If a ruler or measuring tape was used, it could be taped to the table, stopping it from moving during the measuring process. It is also possible that standing above the measuring tool directly could make for more accurate results because the point of view would be better.

<span style="font-family: Arial,Helvetica,sans-serif;">Representing Constant Motion (9/12/11)
<span style="font-family: Arial,Helvetica,sans-serif;">Data: <span style="font-family: Arial,Helvetica,sans-serif;">

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

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

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

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

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

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

<span style="font-family: Arial,Helvetica,sans-serif;">Discussion Questions:
 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">How can you tell that there is no motion on a…
 * 2) position vs. time graph
 * 3) the position line should be a straight horizontal line indicating no change in position and there is equal space between each point.
 * 4) velocity vs. time graph
 * 5) the velocity line should also be a straight horizontal line because the velocity is constant at zero.
 * 6) acceleration vs. time graph
 * 7) the line should be a horizontal straight line because there is no acceleration done at rest, indicating that the slope is 0.


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">How can you tell that your motion is steady on a…
 * 2) position vs. time graph
 * 3) the line should be steadily going up on a consistent slope with the points equally spread apart.
 * 4) velocity vs. time graph
 * 5) this will be a straight horizontal line because the velocity is not fluctuating.
 * 6) acceleration vs. time graph
 * 7) the acceleration line should be straight and horizontal because there is no acceleration at constant speed.


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">How can you tell that your motion is fast vs. slow on a…
 * 2) position vs. time graph
 * 3) if an object is moving faster, the slope will be greater. Steeper slopes will mean faster movement.
 * 4) velocity vs. time graph
 * 5) the higher the value for velocity means the faster the person is moving because the time is the same for slow and fast movement but velocity is displacement over time and if the person is moving faster they were displacing more distance over time, equaling a higher velocity.
 * 6) acceleration vs. time graph
 * 7) the acceleration time should be a horizontal line because assuming the person is at constant speed there is no acceleration. You can't tell how fast the person is going if they are at constant speed.


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">How can you tell that you changed direction on a…
 * 2) position vs. time graph
 * 3) the slopes will be opposite (the signs will change)
 * 4) velocity vs. time graph
 * 5) it is shown that direction is changed if the velocity over time reaches the starting velocity. This is because the velocity is displacement over time and if the person is coming back or changing direction they are displacing less distance and will have a smaller velocity again.
 * 6) acceleration vs. time graph
 * 7) Accleration can't be shown beccause it is not depedant on direction. Again, it should be constant horizontal line at a constant speed.


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">What are the advantages of representing motion using a…
 * 2) position vs. time graph
 * 3) The position time graph is very helpful because it shows the change in direction. It can also show if an object is traveling at constant speed because the points will be an equal distance apart.
 * 4) velocity vs. time graph
 * 5) the velocity time graph shows if you are moving at a constant speed. It can also show changes in direction because it is displacement over. It is very detailed so it helps to calculate rate.
 * 6) acceleration vs. time graph
 * 7) similar to velocity vs. time graph, the acceleration is helpful with calculations because it is so detailed. It shows if an object is speeding up or slowing down.


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">What are the disadvantages of representing motion using a…
 * 2) position vs. time graph
 * 3) it is harder to do calculations using this graph. It can't give you actual velocity or acceleration. It can only show estimates.
 * 4) velocity vs. time graph
 * 5) It does not show the starting point or distance. Also, calculations must be done to find other information. It is difficult to use because it is hard to keep at a steady motion.
 * 6) acceleration vs. time graph
 * 7) Similar to velocity, it is difficult to use this graph because it is hard to keep at constant motion. It also does not show that much information.


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">Define the following:
 * 2) No motion
 * 3) No motion is the absence of acceleration or distance. The object is not moving so it has no total distance or acceleration.
 * 4) Constant speed
 * 5) Constant speed has no acceleration but is categorized by an object moving at a constant rate over any distance. All calculations, such as instantaneous speed, should be the same as the average, such as average speed.

<span style="font-family: Arial,Helvetica,sans-serif;">Lab Acceleration Graph (9/14/11)
<span style="font-family: Arial,Helvetica,sans-serif;">Lab partner: Michael Solimano <span style="font-family: Arial,Helvetica,sans-serif;">**Objectives:** <span style="font-family: Arial,Helvetica,sans-serif;">**Procedure**: <span style="font-family: Arial,Helvetica,sans-serif;">media type="file" key="My First Project.m4v" width="300" height="300"
 * <span style="font-family: Arial,Helvetica,sans-serif;">What does a position-time graph for increasing speeds look like?
 * The slope of the graph will be increasing as the car is accelerating. It will look like a curve.
 * <span style="font-family: Arial,Helvetica,sans-serif;">What information can be found from the graph?
 * You can see how the speed is increasing. The change in slope tells you the change in speed over an interval.

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

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

<span style="font-family: Arial,Helvetica,sans-serif;">**Analysis:** <span style="font-family: Arial,Helvetica,sans-serif;">a) Interpret the equation of the line (slope, y-intercept) and the R2 value. <span style="font-family: Arial,Helvetica,sans-serif;">b) Find the instantaneous speed at halfway point and at the end. (You may find this easier to do on a printed copy of the graph. Just remember to take a snapshot of it and upload to wiki when you are done.) <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">c) Find the average speed for the entire trip.
 * <span style="font-family: Arial,Helvetica,sans-serif;">For the car going down the incline, the R2 value is .999, which means that there were a lot of data points that fit the expected trend line for a polynomial. The R2 value of trend line that was linear was only .9086 which shows that the equation fits better with polynomial points because the car is accelerating rather than at constant speed. The equation of the line is y = 15.262x2 + 3.3291x. The standard equation is y = Ax2 + Bx. The A is ½ of the acceleration value and B is the initial velocity based on the equation d= Vit+ ½at2. The initial velocity should theoretically be 0 or very close to it, but we may have started measuring points when the car was already going down the hill. The y intercept is set to 0 because at 0 time, the position is 0.
 * <span style="font-family: Arial,Helvetica,sans-serif;">For the car going up the incline, the R2 value is .993, which again means that our results are good because it shows that the results almost exactly fit the trend line. The equation for this was y = -21.698x2 + 57.435x. The A value is negative because acceleration is negative which means that the car is slowing down, and the initial velocity, or B value, is so high because the calculations started in the middle of the ticker tape to see where the speed started to decrease. The y intercept is set equal to 0 because at 0 time the cart is at 0.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Going down the track:
 * [[image:Photo_on_2011-09-14_at_10.15.jpg]]
 * <span style="font-family: Arial,Helvetica,sans-serif;">Going up the track:
 * [[image:lab.jpg]]

<span style="font-family: Arial,Helvetica,sans-serif;">**Discussion Questions:** <span style="font-family: Arial,Helvetica,sans-serif;">**Discussion**:
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What would your graph look like if the incline had been steeper?
 * If the incline were steeper, the slope would be larger because the cart would be moving much faster down the incline, so it would accelerating more. If the incline were steeper, the cart going up the ramp would have a less steep line because it would be harder to move up the ramp, so it would be decreasing speed faster and would be moving at a slow pace.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What would your graph look like if the cart had been decreasing up the incline?
 * [[image:Screen_shot_2011-09-14_at_11.01.15_AM.png]]
 * This is the graph of the cart decreasing up the incline. It is accelerating because I pushed the cart, but as it starts to feel the effects of the incline, the speed is decreasing, which is why the slope starts going down.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Compare the instantaneous speed at the halfway point with the average speed of the entire trip.
 * The instantaneous speed was 20 cm/s while the average speed was 18.59 cm/s. This means that at the half way point, the speed was higher than the average speed. This makes sense because to create an average some points must be below and some must be higher.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?
 * A straight line has a continuous slope, or velocity. Because the line tangent to the acceleration graph is only hitting one point, and the velocity is continuous, it can be assumed that the slope throughout the entire line will be equal to the velocity of that one point. If the line was not continuous, like the graph, the slope would not be equal to the point because our graph is curved, which is why a tangent line has to be drawn.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
 * [[image:Screen_shot_2011-09-14_at_6.43.51_PM.png]]
 * [[image:Screen_shot_2011-09-14_at_6.44.08_PM.png]]

<span style="font-family: Arial,Helvetica,sans-serif;">The results of this lab supported the hypothesis I created. My hypothesis guessed that an increasing speed graph would resemble a curve. This was suggested by looking at the graph and because the trend line and equation are polynomial, which has a curved graph line. This happens because the slope gets steeper as the object, in this case a cart, is moving faster because it has a greater velocity. I also hypothesized that the position time graph can show changes in speed because the graph shows the different changes in distance over time. I found that my results are relatively accurate based off of my analysis in the previous questions. It is possible that error occurred when placing the ramp on the book. If the ramp was too far back, the incline might have been either steeper or shallower than expected. Also, when measuring the points, it is possible that the ruler or ticker tape moved. It is also possible that the angle that the ruler was being looked at from changed the perception of the points, making them different than they actually are. To eliminate the error when putting down the incline, an exact measurement on the book could be done as to where to place the ramp. The point of view could also be changed with a different measuring tool or spot that the measurements were taken.

<span style="font-family: Arial,Helvetica,sans-serif;">A Crash Course Lab (9/21/11)
<span style="font-family: Arial,Helvetica,sans-serif;">Michael Solimano, Jake Aronson, Danielle Bonnett <span style="font-family: Arial,Helvetica,sans-serif;">Purpose: <span style="font-family: Arial,Helvetica,sans-serif;">** Objectives ** :
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">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: Arial,Helvetica,sans-serif; font-size: 16px;">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: Arial,Helvetica,sans-serif;">Procedure: <span style="font-family: Arial,Helvetica,sans-serif;">media type="file" key="New Project - Mobile.m4v" width="300" height="300"

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

<span style="font-family: Arial,Helvetica,sans-serif;">Data: <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">Discussion Questions:
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">Where would the cars meet if their speeds were exactly equal?
 * 2) If they were crashing, they would meet at exactly 300 cm or 3 m because if they were equal they would be moving the same speed, and meet in the exact middle of the 600 meters.
 * 3) If they one was catching up to the other but one had a 1 m or 100 cm head start, they would never meet because they are going the exact same speed so the first car would always be 100 cm ahead.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">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.
 * 5) [[image:Photo_on_2011-09-21_at_09.40.jpg]]
 * 6) [[image:Photo_on_2011-09-21_at_10.01_#2.jpg]]
 * 7) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">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?
 * 8) [[image:Photo_on_2011-09-22_at_08.17.jpg]]

<span style="font-family: Arial,Helvetica,sans-serif;">Percent Error and Percent Difference: <span style="font-family: Arial,Helvetica,sans-serif;">Crashing: <span style="font-family: Arial,Helvetica,sans-serif;">Catching Up:
 * <span style="font-family: Arial,Helvetica,sans-serif;">[[image:Photo_on_2011-09-21_at_10.17_#2.jpg]]
 * <span style="font-family: Arial,Helvetica,sans-serif;">[[image:Photo_on_2011-09-21_at_19.40_#2.jpg]]
 * <span style="font-family: Arial,Helvetica,sans-serif;">[[image:Photo_on_2011-09-21_at_10.17_#3.jpg]]
 * <span style="font-family: Arial,Helvetica,sans-serif;">[[image:Photo_on_2011-09-21_at_20.20.jpg]]

<span style="font-family: Arial,Helvetica,sans-serif;">Conclusion:
 * <span style="font-family: Arial,Helvetica,sans-serif;">I chose to do both percent error and percent difference to describe my data sets. This is because I felt it would be the most accurate depiction of the data. Although our percent error is high, indicating that the experimental data did not match with the theoretical data, the percent differences were very small. I feel that this is important because it shows that our trials were repetitive. This might mean that our theoretical is off because the batteries in the CMV were either too old or too new compared to the last time we calculated the velocity. It is also possible that the data has a high percent error because the CMV would move on a slant when it was let go. This makes the crashing points hard to depict and can also cause the data to be misinterpreted. The purpose of this experiment was met because we found that they met between 211.5 cm- 227 cm and Car 2 passed Car 1 anywhere between 58.5 and 80 cm. If I were able to change the experiment to create more accurate results, I would first make sure that CMVs are going in straight lines. The data may be skewed because they were moving on a diagonal. I also would have made sure that the CMVs were accurate, because while Mike and my CMV was labeled, the writing on Danielle and Jake's CMV was scratched off so we were not sure which CMV was theirs. Lastly, I would find a more accurate way of measuring such as video taping and stopping the video to try to identify the point where they met/passed. We were using our finger to estimate where they met, but with human reaction there is always error.

<span style="font-family: Arial,Helvetica,sans-serif;">Egg Drop Lab (9/30/11)
<span style="font-family: Arial,Helvetica,sans-serif;">Final Project: <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;">Brief Discussion of my Results: <span style="font-family: Arial,Helvetica,sans-serif;">The final prototype for our egg drop did not work. We created a box of straws with an X of straws that has newspaper around it. Under the box containing the egg are two balls of paper and another layer of straws. The intention of the lower layer the straws and paper was to help lower the intensity of the impact of the crash.

<span style="font-family: Arial,Helvetica,sans-serif;">Calculations for Acceleration: <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;">Why the Egg Broke: <span style="font-family: Arial,Helvetica,sans-serif;">I believe that our egg broke because the impact of the crash caused the egg to fly upward and it hit the roof of straws and cracked. Even though the structure was stable, it did not absorb enough of the impact of the fall to keep the egg safe. We tried to make the structure with a greater width to take the fall father than height which would have been smarter.

<span style="font-family: Arial,Helvetica,sans-serif;">What we would do Differently: <span style="font-family: Arial,Helvetica,sans-serif;">If we were to redo this project, we would have gone with our original plan which was a cone. By combining our first three prototypes, I feel we would have had a structure that would keep the egg safe. We had started with just a paper cone which caused the egg to bleed and then a straw cone which splattered the egg. A taller cone with some straws on the outside I feel would have worked because it would be able to crush the tip without actually harming the egg. I also think a parachute would have been helpful to slow down its acceleration rate and lessen the fall.

<span style="font-family: Arial,Helvetica,sans-serif;">Free-fall Lab (10/5/11)
<span style="font-family: Arial,Helvetica,sans-serif;">Purpose: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">What is the acceleration of a falling body?

<span style="font-family: Arial,Helvetica,sans-serif;">Hypothesis: <span style="font-family: Arial,Helvetica,sans-serif;">The acceleration should be 9.8 m/s2 because that is the acceleration of gravity. I expected the v-t graph to look like a straight line in the negative section of the graph because it is falling from a high distance downward.

<span style="font-family: Arial,Helvetica,sans-serif;">Data: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Individual Data <span style="font-family: Arial,Helvetica,sans-serif;">

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<span style="font-family: Arial,Helvetica,sans-serif;">Percent Difference and Percent Error: <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">Discussion:
 * 1) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">Does the shape of your v-t graph agree with the expected graph? Why or why not?
 * 2) It does not agree with what I thought because I thought that it was going to be in the negative section. The reason that it is not is because when we were measuring the ticker tape we did not count negative direction so the line is all in the positive section.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">Does the shape of your x-t graph agree with the expected graph? Why or why not?
 * 4) Yes, I thought that it was going to look like a curve upward because it is accelerating so the position is increasing.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)
 * 6) Compared to the actual supposed acceleration of 981 cm/s^2, the data we collected was not very good. There was an 18.64% difference between the expected data and the observed data, but compared to the rest of the class, the data we collected was not bad. The percent difference was 4.92% which means the data we collected was only about 5% off from the data the rest of the class collected. This makes sense because almost nobody would have a slow percent error because the friction created by the spark timer will slow the acceleration meaning that nobody would get 981 cm/s^2 but our data was similar to all of the other groups, which means that the data was good for the circumstances.
 * 7) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">Did the object accelerate uniformly? How do you know?
 * 8) The object did not accelerate uniformly because if it did the r value would be 1. This is because the slope between every point would be the same and the line would be perfectly linear. Because this is not the case, it can be concluded that the acceleration was not uniform. The object, however, was very close because the r value was almost 1 and the trend line of the graph was linear.
 * 9) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?
 * 10) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px;">The factors that would make the acceleration higher than it should be is if there was a force pushing down on the object like air, but this should not have happened. It would also be higher if something was pulling on the object to make it move faster. The acceleration due to gravity could be lower than it should be because of the friction of the tape rubbing along the spark timer. This will slow down the free fall of the object, therefore slowing the acceleration.

<span style="font-family: Arial,Helvetica,sans-serif;">Analysis of Graphs:
 * <span style="font-family: Arial,Helvetica,sans-serif;">The position vs. time graph looked very similar to what I had predicted in my hypothesis. This is because the free falling weight was accelerating as it continued downward. This means that it should have looked like a J-curve, which it does. The equation for our graph was y=391.86x^2 - 60.111. On the position time graph the y-intercept should have been set to 0, which it was, because at 0 time or the beginning, the position was 0. The equation of the line comes from y=Ax^2+ Bx, which is derived from y = 1/2at^2 + v i t. This means that the slope, or in our case, 391.86 doubled should be equal to our acceleration. This would come to 783.72, but our slope is actually higher. The reason that these are not actual equal is because the velocity time graph could not have a y intercept equal to 0 (will be discussed in second analysis) and therefor they have slightly different numbers. The r^2 value for the graph is .99932 which means that the trend line fit the data very well which means that our data is significant and it generally means that it was done well.
 * <span style="font-family: Arial,Helvetica,sans-serif;">The equation in our velocity time graph is y=798.13x - 63.215 with an r^2 value of .99117 which shows that our data had a very good linear trend line. This graph does not fit my hypothesis because I had thought it would curve upward instead of downwards. In reality, these graphs are the same but we did not measure starting from 0, so none of the values are negative, therefor, it curves up. The equation comes from v f = v i +at where A is equal to acceleration. Because this graph is of a free falling object, the slope should have been 981 cm/s^2 but instead ours was 798.13 cm/s^2. This probably occurred because the ticker tape was going through a spark timer. As the tape went through the spark timer, there was friction which meant that the fall of the object is slowed down. This would lower our acceleration, or slope, as it did for our results. Also, the y intercept cannot be set to zero because there was no way to drop the weight just as the spark timer started, which means that there was no way to make velocity 0 and 0 second, so the y intercept is therefor not zero. By the time that the first dot came the object could have either already been in motion or could have still been at rest. The trend line is linear because the object should be at constant velocity.

Conclusion:
 * My lab results were successful because they supported my hypothesis. The velocity time graph had a lower slope than it should have been and this is possible because of the friction caused by the ticker tape going through the spark timer. Because another force is acting upon the object, it is technically not free fall. The percent error in my lab was significant, but the percent difference was small which indicates that the data was actually very good compared to the rest of the class who also has a problem with friction. It is possible that another source of error besides the friction is that the tape moved when we were measuring since it was difficult to keep down the tape and it would throw off the data. To change this lab, I would use a motion detector instead of the ticker tape. This would eliminate the friction of the weight moving through the spark timer, and would also create the graph of what the free fall looked like with accurate distances.