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CBL
Lab 5

Graphing Distance vs. Time 

Goals:

1.  To use the calculator to make a distance vs. time graph, and
2.  To determine the relationship between a distance - time graph and speed

Materials:

TI-82 or TI-83 calculator

Introduction:

Jill walks forward while Bob records her distance from where she started at one second intervals. The data recorded are listed below. Using the recorded data, Jillís average speed during any time interval can be determined using the definition:

average speed  =  distance traveled divided by time traveled.

Another way to examine the data is to construct a distance vs time graph. The steepness of the graph gives you information about Jillís speed.


Data

The following are Bobís recorded data.

Total Time

Total Distance

Total Time

Total Distance

(s)

(m)

(s)

(m)

0.0

0.0

8.0

8.5

1.0

1.0

9.0

13.0

2.0

2.0

10.0

17.5

3.0

3.0

11.0

22.0

4.0

4.0

12.0

24.0

5.0

4.0

13.0

26.0

6.0

4.0

14.0

28.0

7.0

4.0

15.0

30.0

Procedure:

To create a list using the TI-82 OR TI-83

1. Press the [STAT] key. (Make sure Edit is highlighted in the EDIT menu)

2. Press [ENTER] or [1]. (This will select the Edit menu; the first entry under list Ll should be highlighted)

If there are data in L1 or L2 use the arrow keys to move the cursor to the list heading, L1, press [CLEAR] then [ENTER]. Move the cursor to the list heading, L2, press [CLEAR] then [ENTER].

3. Enter 0 for the first time data value; (note that the value that you are entering appears on the bottom line)

4. Press [ENTER].

5. Enter the remaining time data in the same manner.

6. Press [>] (right arrow key; this moves the cursor to the first entry of list L2)

7. Enter the position data in L2. (check to see that both Ll and L2 have the same number of entries)

To make corrections to a list:

Press [STAT] [ENTER] ), use the arrow keys to position the cursor over the entry that you wish to modify; type in the new entry and press [ENTER]

To graph one data list vs. another:

1. Press [2nd][STATPLOT] (this command displays the STAT PLOTS screen; note that there are three possible plots available)

2. Press [1] (this command displays the Plot1 screen)

3. The 5 options you may select are:

a) On vs. Off On indicates that the plot information selected will be activated when [GRAPH] is pressed; to turn On, position cursor over On and press [ENTER] Off indicates that this screen will not be activated when [GRAPH] is pressed

b) Type choices are (in order): scatter plot, line/curve connecting data points, box plot, and histogram (select the second choice - connecting data points)

c) Xlist determines which list will be plotted on the X (horizontal axis); to select list L1 on TI-82, use arrow keys to move flashing cursor over desired list; press [ENTER] (highlighted non-flashing entry is selected); on TI-83 simply enter L1.

d) Ylist determines which list will be plotted on the Y (vertical axis); to select list L2, use arrow keys to move flashing cursor over desired list; press [ENTER] (highlighted non-flashing entry is selected); on TI-83 simply enter L2.

e) Mark determines shape/size of data point markers on the graph

4. After selecting the desired options (remember to turn the plot ON !), press [GRAPH]

5. Your graph may not display all of your data points (because the graphing window is not set properly); press [ZOOM] [9] to automatically select a window that displays the full range of your data.

Name_______________________

Date________________________

Graphing Distance vs Time

Lab Report

Analysis:

1. What quantity is plotted on the y-axis?___________________________________________

On the x-axis?_______________________________________________________________

2. On the given axes sketch the graph as seen on your screen. Label the axes.

3. Sometimes dividing a graph into regions make it easier to analyze. Look for patterns in the data. Examine your graph and draw vertical lines that divide it into regions. How many different patterns did you mark? __________________

4. Using the TRACE function and arrow keys to look at your graph,what was Jill doing during the time interval 4sec-7sec? What was Jillís average speed during that time? Describe the shape of the graph for this time interval. __________________________________________________________________________

__________________________________________________________________________

5. What was Jillís average speed for:

(A) the first four seconds?___________________________________________

(B) the time interval 7 seconds to 11 seconds?____________________________

(C) the last four seconds?___________________________________________

(D) the entire trip? _________________________________________________

6. Suppose the distance for 16s was 29m. Describe the motion of Jill during that time.

_________________________________________________________________________

Conclusions:

7. Look at your answers in #4 and #5 above. What conclusion can you draw about the relationship between the shape of the distance time graph and Jillís speed?

_________________________________________________________________________

8. Why might you prefer to show the data on a graph instead of in a table?

________________________________________________________________________

 

copyright 2009 The North Carolina School of Science and Mathematics