Modeling Constant Accelerated Motion in 1DIn this virtual lab, you will be asked to analyze raw data from a simple motion-cart experiment and model these data points by fitting them to an appropriate curve. The experiment consists of a motion cart which is connected to a hanging mass by a very light (massless) string and pulley system as shown in the figure above. A motion sensor and photogate allow the position and timing information for the motion of the cart to be recorded, and from this the velocity and acceleration can be extrapolated. The aim of the experiment is to reproduce the familiar curves of 1D constant-accelerated motion that we've been using in class (Kinematic Equations), and to learn how to use the curves obtained from the data to obtain the objects acceleration, initial velocity, and initial position. You will then be asked to answer a few questions based on what you've learned!Please read the following instructions for how to complete and turn-in the lab carefully. This lab may be completed either as an individual report, or you may choose to work with your classmates in groups of no more than 4 people to produce a group report. If you choose to work as a group, please provide a list of all group members at the top-left margin of your report, and provide a brief description of how the work on the report was divided. Lab Instructions : Download and read the following following Lab-write up. This would be the instructions for the lab were you to complete the labs in-person. Although you will not be doing the set up yourselves, use this to get an idea for how the experiment is set up and carried out :Lab Worksheet (DOC) // Attached belowLab Worksheet (PDF) /// Attached belowAfter reading a description of the lab set-up, please watch the following short video of me and Professor Inman completing the experiment in the physics lab! Play media comment.// Linked here //In the video, you can see the graphs produced by the PASCO software. The experiment was carried out for 3 separate runs, with each run having a mass of m = 15g, 25g, and 35g, respectively. The raw data for each of these three runs has been arranged in an excel (or PDF) spreadsheet for you to work with here : (each run is contained in a separate sheet) Lab 1 Data File (Excel) // Attached BelowLab 1 Data File (PDF) //Attached BelowUse these data files to produce scatter plots of the position vs. timevelocity vs. timeacceleration vs. time data for each of the three runs. You should produce a total of 9 graphs, three (position, velocity, acceleration) for each of the three runs. You may use the original data files to display your graphs, or copy them to a separate lab write-up file. Each graph should be clearly labeled, with the appropriate mass for the run and labels for the axes. You may find information on how to produce a graph from a table of date in Excel or in Numbers here :Making a Scatter Plot in Excel (Links to an external site.)Making a Scatter Plot in Numbers (Links to an external site.)Taking the graphs you have produced, fit the appropriate curve to each graph based on what functional relationship (linear, quadratic, exponential, etc.) you expect based on your knowledge of the kinematic equations discussed in class. You may do so by adding a trendline to your data as outlined below. Please make sure to clearly display your trendline with the fit coefficients on your finished graphs. Adding a Trendline in Excel (Links to an external site.)Adding a Trendline in Numbers (Links to an external site.)You will notice that each trendline will have an "R-squard" value quoted. Please watch the following video below if you are unfamiliar with what this variable measures. You will be asked to answer a question on how close your fits model the data based on your R values.Submission InstructionsAfter completing the above steps, you will submit your lab write-up as a file upload directly to this assignment. You may either do so as a group outlined above or individually. Your lab write-up should include the following :Your 9 graphs produced from the data files, either in the original Excel data file. (Please rename the file to clearly identify whose work it is.)A brief (1-2 page) write-up, either in a joint file with your graphs, or as a separate word doc or pdf, commenting on what you learned from the lab. Your write-up should include, but not be necessarily limited to, responses to the following set of questions : What difference, if any, did you notice when watching the video between the 15g run and the 25g run? Can you find any concrete evidence in your data to support your observation? What happens as you increase the hanging mass? What mathematical relationships did you find that best fit the data for your position, velocity and acceleration graphs? How can you quantify the "goodness" of fit in each case? (Comment on the R-values for your fits).Based on your answer to part 2, do you believe the experiment confirmed the simple models for 1D motion that we've been using in class? If not, what deviations do you observe?Comparing the form of your fit equations to the kinematic equations, calculate and make a small table with the initial positions, initial velocities and accelerations for each run.Which of the graphs looked cleanest? Which was noisiest? Why might you think this is? (Think of how the data is collected). Please submit these files directly through this assignment. The files are due by midnight the night before the first exam.

Please could you check this work for errors and make suggestions for amendments where needed.

InstructionsPart B of this exercise involves examination of time series data for atmospheric CO2 concentrations at Mauna Loa, Hawai’i. The first website for accessing these data (Mauna Loa CO2 (Links to an external site.)Links to an external site.) presents:Recent monthly mean CO2 at Mauna Loa: monthly values for atmospheric CO2 concentrations at Mauna Loa over the past five years (since 2014 - red line) and these same values corrected for the average seasonal cycle (black line).The second website presents a longer-term record of CO2 concentrations since measurements began. It can be accessed using the tab entitled Full Record above the 5-year monthly mean graph:Full Mauna Loa CO2 (Links to an external site.)Links to an external site. record: long-term trend in monthly values for atmospheric CO2 concentrations at Mauna Loa since measurements began in 1958 (red line) and seasonally corrected data (black line).The third website presents information on the growth rate of atmospheric CO2 concentrations since measurements began. It can be accessed using the tab entitled Growth Rate above the 5-year monthly mean graph:Annual mean growth rate for Mauna Loa, Hawaii (Links to an external site.)Links to an external site.: a histogram of the annual increase in atmospheric CO2 concentrations at Mauna Loa since measurements began in 1958 (turquoise vertical bars) and decadal averages (black horizontal lines).QuestionsQuestion 1 5 ptsDescribe the annual pattern of fluctuations shown by the red line in the graph entitled “Recent monthly mean CO2 at Mauna Loa” specifying the timing and value of high and low concentrations plotted.A strong answer will specify the timing and values of highest and lowest concentrations, noting units, and the typical range of annual fluctuations, describing the overall trend and CO2 values in terms of persistent patterns.Question 2 5 ptsWhy do the values of atmospheric CO2 concentrations show annual fluctuations?A strong answer will describe the annual variation in terms of difference in CO2values and the timing of the change and explain why the CO2 values exhibit annual fluctuations based on seasonal variations in plant uptake of CO2 and its subsequent release.Question 3 5 ptsWhat is the overall increase in CO2 shown by the black line in the graph entitled “Recent monthly mean CO2 at Mauna Loa” over the 5-year time period represented?A strong answer will report specific CO2 concentrations over the past 5 years, noting units, and use quantitative data citing pertinent values in the comparison of the different years.Question 4 5 ptsIs the difference in CO2 concentrations between October 2018 and October 2017 noted numerically in the green box above the graph (Monthly Average (Links to an external site.)Links to an external site.) comparable to the annual increase over the past 5 years?A strong answer will report specific CO2 concentrations over the past 5 years, noting units, and use quantitative data citing pertinent values in the comparison of the past years' increase to that in previous years.Question 5 5 ptsWhat is the overall increase in CO2 shown by the black line (seasonally corrected data) in the graph entitled “Atmospheric CO2 at Mauna Loa Observation” since records began in 1958? A strong answer will report specific CO2 concentrations, noting units, and comment on the overall trend in the longer time series data in terms of the increase in concentration in ppm and as a percentage of the 1958 value.Question 6 5 ptsHow does the annual increase in CO2 concentrations over the past 5 years (previous question) compare with the annual average increase in CO2concentrations over the 59-year record?A strong answer will report specific CO2 concentrations, noting units, and comment on the overall trend in the longer time series data, comparing the average long-term increase with that observed over the past 5 years .