1. Lab Extension Purpose: To create graphical and mathematical representations of the relationship between the velocity and the time for a disk rolling down an incline. Time ( s ) Velocity ( cm/s ) 00 2.0 4.0 6.0 8.0 10. 12 14 16 18

2. Finding Slopes of Tangent Lines with TI Calculators First you must enter the position math model from your lab. TABLE 1 TI-83 / 84TI-86TI-89 y=Graph Green Diamond y(x)= [F1]Y= [F1] Enter the position math model your group developed in the lab. If other equations are already on your calculator, either clear these equations or simply unselect them.

3. Finding Slopes of Tangent Lines with TI Calculators Next you need to set the graph window so that you will see your top-opening parabola. TABLE 2 TI-83 / 84TI-86TI-89 WindowGraph Green Diamond Window [F2] Use the following guide to set your graph range. Xmin = 0Ymin= -20 Xmax= 20Ymax= 150 Xscl = 0.1Yscl= 0.1

4. Finding Slopes of Tangent Lines with TI Calculators Now it is time to tell the calculator you want it to find the slope of the tangent line at a particular point on your graph. TABLE 3 TI-83 / 84TI-86TI-89 GraphGraph [F5]Green Diamond Draw [2 nd ][Pgrm]MoreGraph [F3] 5: TangentMath [F1]Math [F5] MoreTangent [Alpha][=] More TANLN [F1] You should now see the graph of your math model (a top opening parabola) with a blinking cursor on it.

5. Finding Slopes of Tangent Lines with TI Calculators TABLE 3 TI-83 / 84TI-86TI-89 GraphGraph [F5]Green Diamond Draw [2 nd ][Pgrm]MoreGraph [F3] 5: TangentMath [F1]Math [F5] MoreTangent [Alpha][=] More TANLN [F1] Next, simply type in the lowest time you measured in your original data. Then press ENTER. The calculator has drawn the tangent line to the graph at your chosen time and reported its slope as either or as the equation of the tangent line from which you can extract the slope. As discussed in class, the slope of this tangent line is the instantaneous velocity of the ball at that time. Record it as such in the data table.

6. Finding Slopes of Tangent Lines with TI Calculators TABLE 3 TI-83 / 84TI-86TI-89 GraphGraph [F5]Green Diamond Draw [2 nd ][Pgrm]MoreGraph [F3] 5: TangentMath [F1]Math [F5] MoreTangent [Alpha][=] More TANLN [F1] Repeat this process beginning with TABLE 3 above and find the instantaneous velocity for each of your times and record in your data table. When you have all ten data points, graph the velocity vs. time in LoggerPro.