University of London Motion in One Dimension Data Analysis Task – Description
1. To do this, open a Microsoft Excel spreadsheet. Create headings for your data (labeling them with appropriate units), then enter your time measurements into the first column and the associated position measurements in the second column.
2. Create a graph with the time measurements along the horizontal axis and the position measurements along the vertical axis. Give the graph an appropriate title. The graph produced here is a graphical model for this data.
3. To determine the mathematical models for the data, we will find best fit lines for data that appears linear and will need to linearize data that is not. The equation of the best fit lines that match linear data are the mathematical models. For each relationship, if it appears to be linear, add a trendline to determine the slope and y-intercept of the best fit line for the data. Use the y = mx + b form for the line to produce the mathematical model, where m is the slope of the best fit line and b is its y-intercept. If your data appears to be linear, skip the next step. 4. For a relationship that appears to be nonlinear, you will need to linearize it. To do this, first examine the plotted data to determine the likely relationship between the variables. You should be familiar with the shapes of some common functions (i.e. quadratic, cubic, etc.), but you may need to find additional resources if your data does not appear to fit the shapes of the functions that you know. Once you’ve identified a function shape that could match your data, you will create a new graph after performing the mathematical operation on your dependent variable that fits the shape of your graph. For example, if your position vs. time data looked similar to a quadratic function, f (x) / x2, you would square the values of your times, then plot a new graph with the squared values on the horizontal axis and your position on the vertical axis.
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