Ch2_TalasH

toc =Lesson 1 - Describing Motion with Words = a, b, c, d

1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.

I already understood what distance and displacement were and the difference between the two. Distance is "how much ground an object has covered" and velocity is "how far out of place an object is." In addition, I already knew about velocity and speed and that speed is a scalar quantity and velocity is a vector quantity. Speed is "how fast an object is moving" and does not refer to a particular direction. Velocity is the "rate at which an object changes position" which means it is direction aware. I also understood the formula: ** Average Speed = __Distance traveled__ **  ** hbjjnbvfdgggffffff time traveled **

2) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.

I understood scalars and vectors but forgot which refers to “size” (or numerical value) and which refers to “size and direction.” Reading the lesson helped clarify that scalar means quantities described with size only and vector means quantities described with size and direction.

3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.

How do time and position change when relating to constant speed and changing speed?

4) What (specifically) did you read that was not gone over during class today?

I do not remember going over instantaneous speed during class. (the speed at any given instant in time). Also we did not learn this formula: ** Average ** ** velocity = __change in position__ = __displacement__ **  ** enjfdjnfnlsnfknkddj elapsed time kdnfsds elapsed time **

=Notes: speed, velocity, distance, and displacement =

 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lesson 2 - Describing Motion with Diagrams = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a, b, c

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">I already understood the vector diagram and how a vector arrow points to the direction that the car is moving towards. It also becomes longer when the car is accelerating. Also If the spark timer device is measured at 10 hertz per second, this means it creates 10 dots every second. In addition I already knew how ticker tape diagrams work. When the trail of dots are farther apart, it means the object is moving faster. Also, the device that places the tick (dot) only measures scalar quantities because it does not show what direction the object is moving towards.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.

<span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">The lesson cleared my confusion of the direction of acceleration. I did not know how to determine when the object will have an acceleration directed in the opposite direction of its motion. Reading the lesson, I saw that it is when the object is slowing down.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.

<span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">There was nothing I specifically did not understand.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) What (specifically) did you read that was not gone over during class today?

<span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">Everything I read was gone over in class today.

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Notes: vector and ticker tape diagrams =

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lab: Speed of Constant Motion Vehicle = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">September 9, 2011 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lab partner(s): Kosuke Seki

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 110%;">__Objectives:__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) How precisely can you measure distances with a meterstick?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) How fast does your CMV move?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) what information can you get from a position- time graph?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__ Materials: __ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) Spark timer <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) Spark tape <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) Meter stick <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) Masking tape <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">5) CMV

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 110%;">__Hypothesis:__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) You can measure distances with a meter stick precisely by measuring to two decimal places in centimeters because the meter-stick is in centimeters.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) The CMV moves 10 cm/s because it didn't move pass my laptop (33 cm) in a second.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) The position of the CMV and the average velocity because the slope on a p-t graph is the velocity.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> __Length of Laptop (cm)__: 33.0 cm

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 110%;">__Data Table: Position of the CMV__ <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 110%;">__Graph:__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 110%;">__Discussion questions:__ <span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) Why is the slope of the position-time graph equivalent to average velocity?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The slope of the position-time graph is equivalent to average velocity because slope = __y____2-y1__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> djnfjkkjlsfnijdakbnfjsdbjfhdsnjsdgcrfghjhgtfdreswdefrgthjhygtfrdeswdefghbgfdefgbgvfcdxsdcfv fs x2-x1 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> and change in position (on the y-axis) divided by elapsed time (on the x-axis) equals the average velocity. If you take (0.0, 0.0) and (0.1, 2.55) and use the slope formula, you will get the instantaneous velocity of those two points. If you continue to do this for the rest of the points, and then find the average of those results, you will get the average velocity which is also the slope.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) Why is it average velocity and not instantaneous velocity? What assumptions are we making?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">It is average velocity because the slope refers to the entire graph and all the values. It is not instantaneous velocity because we are measuring the velocity at ten different instances in time and averaging them together, we are not finding the velocity at one instant in time. We are assuming that the vehicle is moving at a constant velocity.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) Why was it okay to set the y-intercept equal to zero?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">It was okay to set the y-intercept at 0 because there was no specific initial point that the CMV had to start at.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) What is the meaning of the R2 value?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">R2 shows if the data is linearly correlated and which direction it's correlated. The closer it is to 1 or -1, the more correlated it is.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">5) 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?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">I would expect it to lie below the original graph and have a smaller slope.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__ Notes (Analysis): __ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">slope = y/x <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">= change in position/ change in time <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">= d/t <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">= velocity

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Possible errors:
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Equipment provided or procedure
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Surface may not be leveled
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">If the ruler moved when measuring
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Ignoring the beginning dots- where you cut it off
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Car may have already been in motion when device was put on

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 110%;">__Conclusion:__

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The CMV moves at 34.951 cm/s; this proves that my hypothesis, 10 cm/s, was inaccurate. I had expected the velocity of the CMV to be slower than it really was. The positon-time graph was used to find the average velocity which is the slope in the equation of the line, 34.951. There are many sources of error that may have contributed to inaccuracies. For example, error may have occurred when choosing which dots to ignore in the beginning of the spark tape. If one did not ignore enough, the CMV would not be at constant velocity in the beginning. Ignoring at least 3 dots would minimize these issues. Another inaccuracy could be that the ruler moved when measuring the distance between the dots on the spark tape. Someone could hold the ruler down to assure no errors were being made.

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Activity: Graphical Representations of Equilibrium =

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) How can you tell that there is no motion on a…
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">position vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">You can tell there is no motion because the graph shows a horizontal line which means there's no slope.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">velocity vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">You can also tell there is no motion because line will be at y = 0.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">acceleration vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">You can also tell there is no motion because the line also be at y=0 which means that the acceleration is not changing.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) How can you tell that your motion is steady on a…
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">position vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> You can tell the motion is steady because the line will have a constant increasing or decreasing slope.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">velocity vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">The line will be horizontal (slope of 0) if the motion is steady.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">This is graph of positive constant velocity

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">acceleration vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">The line will be y=0 if the motion is steady.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) How can you tell that your motion is fast vs. slow on a…
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">position vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">The slope of the line for fast motion will be steeper than the slope of the line for slow motion.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">velocity vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">For constant velocity, the horizontal line for fast motion will be above the horizontal line of slow motion.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">acceleration vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">At constant speed, there is no acceleration, so on a a-t graph you would not be able to see if your motion is fast or slow.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) How can you tell that you changed direction on a…
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">position vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">You can tell that you changed direction because the line has a negative slope when walking towards and a positive slope when walking away from the device.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">velocity vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">If the object is going in a positive direction, then it will be in the positive region. If the object is going in a negative direction, then it will be in the negative region.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">acceleration vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">You cant tell if you changed directions when at rest or constant speed.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">5) What are the advantages of representing motion using a…
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">position vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">This will give you a way to show how much distance you've made at a certain time.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">velocity vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">This will show you the rate of speed you are going at at a certain time.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">acceleration vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">This will show you how much your accelerating at a certain time.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">6) What are the disadvantages of representing motion using a…
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">position vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">You can only determine the average velocity by looking at the slope of the graph; and not the velocity between two points.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">velocity vs. time graph
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">You can only determine the acceleration by looking at the slope of the graph; not the acceleration between two points.
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">acceleration vs. time graph
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">You can't tell direction unless the person walking is accelerating.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">7) Define the following:
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">No motion
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">This means the person is "at rest"
 * 1) <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">Constant speed
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">This means the person is walking at a steady pace.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**__Constant Fast and at rest__**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**__Constant slow and at rest__**

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> =

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Notes: at rest and constant speed graphs =

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lesson 1 - e =

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">I already understood the formula for acceleration and that it is the rate of the change of velocity over time. <span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">In addition, I already knew that the direction of acceleration is opposite the direction of the velocity when the object is slowing down.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">I was slightly confused why the acceleration of an object could have the unit of m/s^s. I now understand that it was simplified from m/s/s.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">Why is it that “an acceleration of -2 m/s/s is an acceleration with a magnitude of 2 m/s/s that is directed in the negative direction”?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4)What (specifically) did you read that was not gone over during class today?

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">We did not learn about the square relationship between distance and time. The distance traveled after 2 seconds is 4 times the distance traveled after 1 second.

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">x-t and v-t graphs of acceleration =

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lesson 3 = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a, b, c

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;"> I already understood that constant positive velocity will have constant positive slope in a position time graph and constant negative velocity will have constant negative slope. In addition, I already knew that a larger velocity has a larger slope. Also, I knew how to tell whether and object is increasing or decreasing in velocity. <span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">On the graph to the left, the slope starts out small and then ends large, meaning this object is increasing in velocity (accelerating). On the graph to the right, the slope starts out large and ends small, meaning it is decreasing in velocity.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">Understanding how to find slope on a position time was easy. All I would have to do is choose two points and plug them into the formula, y2-y1/x2-x1

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">The reading clarified that all the properties that the velocity of a graph has is the same as the slope and how positive changing slope is a positive changing velocity (acceleration) on a position time graph. It also clarified that a curved line on a position time graph represents changing velocity. I did not know how changed velocity was drawn on a p-t graph before.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">I understood the entire reading.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) What (specifically) did you read that was not gone over during class today?

<span style="color: #5c0d5c; font-family: 'Times New Roman',Times,serif; font-size: 110%;">It was all gone over in class.

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lesson 4 = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a, b, c, d, e

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">I understood that changing velocity (acceleration) results in a slope while constant velocity has no slope. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">I was confused about finding the direction of velocity. I now know that positive velocity = positive direction (when in the positive region) and negative velocity = negative direction (when in the negative region). If the line crosses the x-axis (from the negative region to the positive region) the the object changed directions. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Also, I did not understand that when the object is moving away from the x-axis, it is speeding up. When the object is moving towards the x axis, it is slowing down.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">I understood everything in this reading.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) What (specifically) did you read that was not gone over during class today?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Everything was covered in class.

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Notes: increasing and decreasing acceleration graphs =

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">For acceleration: If the line is located in the negative region of the graph, then the object is moving in a negative direction. If the line is located in the positive region of the graph, then the object is moving in a positive direction. If the line goes from a negative region to a positive region, then the object changed directions.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lab: Acceleration Graphs = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">September 16, 2011 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lab partner(s): Kosuke Seki

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Objectives:**
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">What does a position-time graph for increasing speeds look like?
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">What information can be found from the graph?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Available Materials:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) Spark tape <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) spark timer <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) track <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) dynamics cart <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">5) ruler/meter-stick/measuring tape

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Hypothesis:** > away from the x axis because increasing speed goes in the positive direction.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">A position time graph for increasing speed will look like a curved line because the velocity will be changing. It will also be
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The acceleration, average velocity, and displacement can be found from the graph because the slope is the acceleration, the average velocity is found by putting displacement over time, and displacement is found by subtracting the initial y value (position) from the final y value (position).

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Analysis:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a) Interpret the equation of the line (slope, y-intercept) and the R2 value. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">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: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">c) Find the average speed for the entire trip. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The linear trend line for increasing acceleration shows that my R2 value was .94 but with a polynomial trend line my R2 value was .999; this means the the polynomial trend line shows better results. The equation for increasing speed is y = 12.438x^2 +9.5866x. Here, y is the change in position, 12.438 is (1/2)a, 9.5866 is initial velocity, and x is change in time. The equation for decreasing acceleration is y = -32.323x^2 + 85.647x. The R^2 value, 0.99995, shows how accurate the trend line is.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">For increasing speed:
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">For decreasing speed:

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Procedure:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) First, my lab partner and I gathered the materials and setup the track by putting a textbook under the track and lining it up to the edge of the book. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) Then we put the spark timer at the top of the ramp for measuring increasing speed. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) Then we put the spark tape through the spark timer end taped the the end of the spark tape to the cart. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) Next we turned on the timer and let the cart go down the ramp. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">5) We removed the tape from the spark tape and put the timer at the bottom of the ramp. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">6) We then put spark tape through the timer and taped it the cart. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">7) Next we turned the timer on and pushed it up the ramp, and let it move back down the ramp. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">8) We then measured the distances between the dots on the tape for increasing speed and decreasing speed. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">9) Next we plotted the data in excel and created a graph with both increasing and decreasing speed on it.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Notes:**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">May have not released the cart when the spark timer made the first dot.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Discussion Questions:**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) What would your graph look like if the incline had been steeper? <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) What would your graph look like if the cart had been decreasing up the incline? <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) Compare the instantaneous speed at the halfway point with the average speed of the entire trip. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense? <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">5) Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The line would be heading upwards on the graph because the velocity would be increasing. It will also end with a steeper slope.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The line would be heading downwards and would end with a smaller slope.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">For the decreasing speed: The instantaneous speed at the halfway point is 40 cm/s and the average velocity is 46.67 cm/s. The average velocity is larger for this line.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">For increasing speed: The instantaneous speed at the halfway point is 26.67 cm/s and the average velocity is 24.17 cm/s. Here the average velocity is smaller.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The instantaneous speed is the slope of the tangent line because your finding the change of y over the change of x

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Graph:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Table:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Conclusion:**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">My hypothesis was that the line for increasing speed will be away from the x-axis and look curved; this was accurate because that is what our results (the graph) show. I also predicted that the a-t graph would show the acceleration which is true because when the equation of the graph was found, the slope was the acceleration. In addition, I said you could find displacement which is true, but you would have to calculate it (y2-y1). A source of error in the experiment could be that we may have not release the cart when the spark timer mad the first dot. A way to prevent this error is to release the cart first and then turn the spark timer on.

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Interpreting Position Time Graphs = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> = =

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Chapter 2: Class Practice Problems (acceleration) =

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lab: A Crash Course in Velocity (Part II) = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">September 23, 2011 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Lap partners(s): Kosuke Seki, Noah Pardes, Michael Poleway <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Theoretical Calculation:**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a) The CMV's will crash at 362.57 cm <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">t = 6.79 s

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">b) The CMV's will crash at 189.78 cm <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">t = 5.43 s

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Available Materials**: <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) Constant Motion Vehicle <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) Tape measure and/or metersticks <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) Masking tape (about 30 cm/group) <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4) Stop watch <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">5) spark timer <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">6) spark tape

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Procedure:** __<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Crash __ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">media type="file" key="Crash Process.mov" width="300" height="300"

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Trial: <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">media type="file" key="Crash 3.mov" width="300" height="300"

__Catch up__ media type="file" key="Catch Up Process.mov" width="300" height="300"

Trial:

media type="file" key="Catch up 2.mov" width="300" height="300"

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Data:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a) <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">b)
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Trial || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Position (that they meet at) ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">369 cm ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">380 cm ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">372 cm ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">360 cm ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Trial || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Position (that they meet at) ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">192 cm ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">180 cm ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">187 cm ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Analysis:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">% Error <span style="font-family: 'Times New Roman',Times,serif;">**( |** theoretical **-** Experimental **| /** theoretical **)** x 100

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">% Difference <span style="font-family: 'Times New Roman',Times,serif;">**( |** average experimental value **-** individual experimental value **|** **/** average experimental value **) x** 100

__<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Crash: __




 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Trial || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Position (that they meet at) || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">% Difference ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">369 cm || 0.34% ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">380 cm || 2.49% ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">372 cm || 0.47% ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">360 cm || 2.77% ||

__<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Catch up: __

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">


 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Trial || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Position (that they meet at) || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">% Difference ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">192 cm || 3.04% ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">180 cm || 3.39% ||
 * 3 || 187 cm || 0.36% ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Discussion questions:**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1) Where would the cars meet if their speeds were exactly equal?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">If the speeds were equal and the cars were going towards each other 600 cm apart, they would meet in the middle at 3 meters. If they were going in the same direction at where one car was 100 cm ahead and their speeds were equal, they would not meet.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2) 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.





<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3) 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: 'Times New Roman',Times,serif; font-size: 110%;">**Conclusion:**

Our calculations compared to our experimental data were extremely accurate. We found that our theoretical value for the crash was 362.57 cm and the average experimental value was 370.25 cm. These results were close and the percent error was only 2.12% and the percent error must be less than 10% for the results to classify as accurate. We also found that the theoretical value for the catch up, 189.78 cm, was very close to the average experimental value, 186.33 cm. Our percent error was 1.25% meaning we had great results. Many sources of error could have contributed to our results. For example, we found that the blue car would often drift off instead of heading straight. In addition, there may have been wrong readings of the distance at which the cars crashed. Also, the cars may have not necessarily “crashed” but instead, they just passed each other. This made it more difficult to find the distance where they met. In order to prevent these errors, we could have put the cars on a track to prevent them from drifting away. In addition, one person could have stood right in front the theoretical distance and checked to see where they crashed.

=**Egg Drop Project**= Partner: Stephanie Wang



Our final project consists of straws, sewing string, paper, and a rubber band. We glued together straws in a way so that they will go in many different directions and created a rectangular inlet that fit exactly the average diameter of an egg. In addition, we created a parachute for more support when the egg and package lands.
 * Our Final Project:**
 * Description:**

The egg inside the package successfully landed intact.
 * Results:**


 * Analysis:**

The acceleration of gravity, 9.8 m/s^2, is much higher than the acceleration we calculated of the package, 2.83 m/s^2. This means that it took more time for the object to land on the ground. Most likely, this is because the parachute we built into the package. This made our acceleration slower.

If I were to remodel this project, I would attempt to use less materials. For example, I could entirely remove the parachute. It seemed that the egg would have safely landed to the ground without the support of the parachute. In the end, this newer project would weigh less and be just as successful.

=Lesson 5 - Free Fall and the Acceleration of Gravity= a, b, c, d, e

A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two characteristics that are true of free-falling objects:
 * Introduction to Free Fall **
 * they do not encounter air resistance.
 * They all accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for //back-of-the-envelope// calculations)

The position of the object at regular time intervals - say, every 0.1 second - is shown on the ticker tape trace. The distance that the object travels every interval of time is increasing and shows the ball is speeding up as it falls downward. If an object travels downward and speeds up, then its acceleration is downward. There is no air resistance in free fall.

ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffrhdjfgytuhsdgetysfncnsihfninrshfiuhnidnfcidjsficnihsfjcijfiosrhngfijierhsgjfoijsiofjoiesnfdisofj **The Acceleration of Gravity** Physicists use the symbol g for the acceleration of gravity downward. The numerical value is 9.8 m/s/s. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. g = 9.8 m/s/s, downward

( ~ 10 m/s/s, downward) To accelerate at 9.8 m/s/s means to change the velocity by 9.8 m/s each second.

The velocity and time for a free-falling object being dropped from a position of rest pattern: The data above reveals that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s/s. The velocity of the ball is seen to increase as depicted in the diagram at the right. The velocity of the ball is seen to increase as depicted in the diagram at the right.
 * **Time (s)** || **Velocity (m/s)** ||
 * 0 || 0 ||
 * 1 || - 9.8 ||
 * 2 || - 19.6 ||
 * 3 || - 29.4 ||
 * 4 || - 39.2 ||
 * 5 || - 49.0 ||

Acceleration is the rate at which velocity changes. In free-fall, it changes by 9.8 m/s every second.

**Representing Free Fall by Graphs** In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. A position versus time graph for a free-falling object is shown below.



Since g = 9.8 m/s/s, there is a curved line on a position versus time graph The small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. The negative slope of the line indicates a negative velocity. A velocity versus time graph for a free-falling object is shown below.



Since g = 9,8 m/s/s, downward, it would be expected that its velocity-time graph would be diagonal. The object is moving in the negative direction and speeding up meaning it has a negative acceleration. T The slope is negative for a free falling object.

The velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen. The formula for determining the velocity of a falling object after a time of t seconds is vf = g * t 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. Example Calculation:At t = 6 s vf = (9.8 m/s2) * (6 s) = 58.8 m/s The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. The distance fallen after a time of t seconds is given by the formula. d = 0.5 * g * t2 Example calculations for the distance fallen by a free-falling object after one and two seconds are shown below. Example Calculation:At t = 1 s d = (0.5) * (9.8 m/s2) * (1 s)2 = 4.9 m  At t = 2 s The diagram below (not drawn to scale) shows the results of several distance calculations for a free-falling object dropped from a position of rest. Distance and velocity are dependent on time.
 * How Fast? and How Far? **

**The Big Misconception** 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. The answer to the question (doesn't a more massive object accelerate at a greater rate than a less massive object?) is absolutely not! Not if we are considering the specific type of falling motion known as free-fall. 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. The acceleration of an object is directly proportional to force and inversely proportional to mass. Increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. The greater force on more massive objects is offset by the inverse influence of greater mass. A All objects free fall at the same rate of acceleration, regardless of their mass.

=Free Fall Class Notes=
 * Mass has nothing to do with the rate of free fall.


 * What is the acceleration at max height?
 * a = -9.8 m/s^2
 * Velocity is 0
 * Freefall: anytime gravity is acting on an object
 * When a ball being thrown leaves your hand and right before it hits the ground is initial and final velocity. There is no initial or final velocity of 0.
 * Any object only acted on by the force of gravity.





=Lab: Free Fall Acceleration Due to Gravity= October 5, 2011 Lab Partner: Kosuke Seki


 * Purpose:**
 * 1) What is acceleration due to gravity?
 * 2) What does a v-t graph of a free falling object look like?
 * 3) How are you going to find acceleration due to gravity from the graph?

1) g=9.8 m/s^2 2) a diagonal line in the negative region of a v-t graph because the object is increasing in velocity in the negative direction. 3) find the slope of the line to find acceleration due to gravity.
 * Hypothesis:**


 * Materials:**
 * 1) Spark timer
 * 2) Spark tape
 * 3) A mass
 * 4) Masking tape


 * Procedure:**
 * 1) Tear off a long un-crumbled piece of tape
 * 2) Thread it through the timer
 * 3) Tape it to the mass
 * 4) Hold it vertically
 * 5) Let if fall and get close to a full second of dots
 * 6) Lay the tape on the floor
 * 7) Find the measurements (8-10) dots to measure


 * Data:**




 * || **v-t graph Class data** ||
 * || 853.72 ||
 * || 861.69 ||
 * || 805 ||
 * || 708.97 ||
 * || 767 ||
 * || 864 ||
 * || 881.5 ||
 * || 887.79 ||
 * || 876.56 ||
 * **average** || 834.03 ||

**Analysis**


 * p-t graph**



Here, the equation of the line is 378x^2 + 30.68x. The **slope**, 378.36, is the average velocity. The **R^2** value is 0.99 which shows how accurate the polynomial trend line is. The **shape** of the graph is a curved line increasing away from the origin. This means that the velocity is changing in the positive direction.


 * v-t graph**



The equation of this v-t time graph is 759.49x. This is the **slope**, which is the acceleration of the mass in cm/s^2. The **y intercept** was not set equal to 0 because the spark tape might not have been at rest when the first dot was made. The **R^2 value** is 0.92 which shows how accurate the linear trend line is. The **shape** of the graph shows a straight increasing line away from the origin, meaning the mass is constantly increasing in acceleration (by 759.49) in the positive direction. It also shows a point that is off compared to the rest of our data.


 * Sample Calculations**




 * Discussion questions:**

1) Does the shape of your v-t graph agree with the expected graph? Why or why not?

My expected v-t graph was a straight line with a negative slope towards from the origin. This partially agrees with the shape of our v-t graph because velocity was increasing, but not in the negative direction.

2) Does the shape of your x-t graph agree with the expected graph? Why or why not?`

My expected x-t graph was a curved line going towards the origin with negative slope and a bigger slope at the end. This also partially agrees with the shape of our x-t graph because the velocity was increasing, but not in the negative direction. In other words, the slope should have been positive in my expected x-t and v-t graphs.

3) How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)

The percent difference comparing the average experimental value (classes's average acceleration) and our experimental value was 8.94%. This means that our results were pretty close to the majority of classes'.

4) Did the object accelerate uniformly? How do you know?

The mass did accelerate uniformly because the v-t graph showed a diagonal straight line meaning there was constant acceleration (except for one point).

5) What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?

Usually, air resistance and altitude can cause acceleration to be lower than it should be. If air resistance or altitude is lower then acceleration due to gravity will be higher than 9.81 m/s^2. If they are higher, then it will most likely be lower than 9.81 m/s^2.


 * Conclusion**

My hypothesis, 981 cm/s^2, was close to our experimental value, 759.49 cm/s^2. This means my hypothesis was partially correct and our results were not as good as they should have been. The expected v-t graph was also mostly correct because the results were the same but they were going in the positive direction. I also stated that I could find acceleration due to gravity by finding the slope of the v-t graph. This is exactly correct because our results showed that the slope of the line was the acceleration that you could also find by calculating (Vf - Vi) / elapsed time. However, the percent error of the experiment was 22.58%. Many errors could have occurred throughout the experiment, for example, acceleration could have been slowed down because of the friction between the tape and the timer.he tape This probably happened because the tape did not necessarily slide through the timer smoothly. This source of error could be avoided if we could slide the tape through when it is directly above the spark timer. Although it will require more equipment to accomplish this, this will reduce friction. Also, the distances between the dots on the spark tape may have been faulty because of dents in the tape. Unfortunately, this is what probably weakened our results because one point on our v-t graph was almost completely out of place compared to the others. This mistake could have been fixed we used another piece of spark tape and did the experiment again.. This will help because if one of the spark tapes gave us wrong data, we could rely on the other one.