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)
0
0
2.0
4.0
6.0
8.0
10.
12
14
16
18
Finding Slopes of Tangent Lines with TI Calculators
First you must enter the position math model from your lab.
TABLE 1
TI-83 / 84
TI-86
TI-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.
  cm  2
x  #
2t

s 
y
#
x2
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 / 84
TI-86
TI-89
Window
Graph
Green
Diamond
Window [F2]
Window [F2]
Use the following guide to set your graph range.
Xmin = 0
Ymin= -20
Xmax= 20
Ymax= 150
Xscl = 0.1
Yscl= 0.1
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 / 84
TI-86
TI-89
Graph
Graph [F5]
Green Diamond
Draw [2nd ][Pgrm]
More
Graph [F3]
5: Tangent
Math [F1]
Math [F5]
More
Tangent [Alpha][=]
More
TANLN [F1]
You should now see the graph of your math model (a top opening parabola) with a
blinking cursor on it.
Finding Slopes of Tangent Lines with TI Calculators
TABLE 3
TI-83 / 84
TI-86
TI-89
Graph
Graph [F5]
Green Diamond
Draw [2nd ][Pgrm]
More
Graph [F3]
5: Tangent
Math [F1]
Math [F5]
More
Tangent [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 dy
or as the equation of the tangent line from which
dx
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.
Finding Slopes of Tangent Lines with TI Calculators
TABLE 3
TI-83 / 84
TI-86
TI-89
Graph
Graph [F5]
Green Diamond
Draw [2nd ][Pgrm]
More
Graph [F3]
5: Tangent
Math [F1]
Math [F5]
More
Tangent [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.