This gives us the average velocity between the time interval from t 1 to t 2 The slope of the secant line can be calculated by the usual method: To obtain the average velocity between two points in time (say t 1 and t 2) we can draw the secant line between these two points and calculate the slope of the secant line. To analyze this function mathematically one would need to take the first derivative of the equation using Calculus.Īt this stage we can still obtain a lot of information from this graph by using graphical analysis techniques. Distance increases in a non-linear fashion. This is a function of the form y = ax 2 + bx + c. We know that the velocity is changing as time goes on because the slope of this line is not constant. This graph illustrates the relationship between the position and the time for an object whose velocity is changing with time. Uniformly Accelerated Motion - Variable Speed - Speed is not constant The slope of this line (the average speed) can be calculated by several methods.ī. Note that "m" is the slope of a straight line (of the form, y = mx + b) and it is constant. This is a typical graph of the relationship between position and time for an object moving at constant speed.īy calculating the slope m of the position-time graph we obtain the velocity of the moving object Uniform Motion - Constant Speed - no acceleration Left click on the axis that needs to be changed and select the new column made with the squared data.A. In the equation box enter ^2 this will square your data in that column. The column name selected will then appear in the equation box. Click the Variables button and select the column name which needs to be squared. To label the units correctly click the down arrow button next to the units box and click superscript and select 2. Label the new column and enter units in the box provided. Click on the Data menu and select New Calculated Column. Using Graphical Analysis to square data 1. Notice the linear fit box gives you the values for the slope and y-intercept. Let go of the mouse and click on the Analyze menu and select Linear Fit. Then drag the cursor to form a gray box, which encloses all the data points. Do this by clicking and holding on an area of the graph near the first plotted point. Using Graphical Analysis to find the slope and y-intercept Next, we must tell the computer to which points we want to “fit” the line. Preforming a linear fit will also give us the y intercept of the line. In Graphical Analysis this is called a linear fit. Instead of finding the slope of this line using the math we can have Graphical Analysis find it for us. Input these values in the table and graphical analysis will automatically plot the graph from the values that were entered. Right click on the graph and select graph options and title the graph Distance vs Time and uncheck connect points. Do the same for the y column name it Distance and give it units of meters or m. Double click on x column on the table and name the x-axis Time and give it units of seconds or s. Double click on that icon to start the program. Inside that folder is program called Graphical Analysis. Using Graphical Analysis to plot a line Using the computers in the Physics Lab (SM252) double click on the physics folder that is located on the desktop. time ” graph distance (m) goes on the y-axis and time (s) goes on the x-axis. x graph put the y values on the y-axis and the x values on the x-axis. The y-intercept will have units of the y-axis. To find the slope of a line using the math method: The y-intercept is where the line crosses the y-axis. The slope will have units of the y axis divided by the units of x-axis. Slope is a measure of how much a line rises or falls from one point on the line to another point on that line. “m” is the slope of the line, and “b” is the y- intercept. Slope and y-intercept: The equation of a linear line is: y = mx+b. Download Introduction to Graphical Analysis and more Physics Lecture notes in PDF only on Docsity!Introduction to Graphical Analysis Objective: To use Graphical Analysis program to graph sets of data and find the line of best fit and to identify and interpret the slope and y-intercept of this line.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |