Name: __________________________________
Excel Exploration Worksheet:
You and your friend decide to take a road trip to North Carolina!
The plan is to drive in the car for 10 hours straight before taking a
break. The Excel spreadsheet tracked your position for the various
hours until you took your first break, along with your average
velocity and acceleration, and accompanying graphs of each are
provided.
Activity 1:
The spreadsheet is setup so you can change the values of the parameters for the slope and yintercept of a linear equation in the form 𝑦 = 𝑚𝑥 + 𝑏. Use the spreadsheet (Sheet 1) to answer
the following questions:
1. Using the linear equation, 𝑦 = 𝑚𝑥 + 𝑏, what does 𝑚 represent in this example? What
does 𝑏 represent?
2. What effect does varying the value of the slope have on the values of the average
velocity?
3. What effect does varying the value of the slope have on the values of the average
acceleration?
Name: __________________________________
4. What effect does varying the value of the y-intercept have on the values of the average
velocity?
5. What effect does varying the value of the y-intercept have on the values of the average
acceleration?
6. In general, how do you calculate the average velocity?
7. In general, how do you calculate the average acceleration?
8. Explain why the graph of the average velocity is a horizontal line. Would this be the case
for all linear equations? Why or why not.
9. Would you expect the graph of the average velocity to look the same for non-linear
functions? Why or why not.
10. Describe the graph of the average acceleration. Would this be the case for all linear
equations? Why or why not.
Name: __________________________________
11. Would you expect the graph of the average acceleration to look the same for non-linear
functions? Why or why not.
Activity 2:
Repeat the above activity, but this time you are given a quadratic equation in the form 𝑦 =
𝑎𝑥 2 + 𝑏𝑥 + 𝑐. In this spreadsheet, you are able to change the values of the parameters for
𝑎, 𝑏, and 𝑐. Use the spreadsheet (Sheet 2) to answer the following questions:
1. What effect does varying the value of the 𝑎 have on the values of the average
velocity?
2. What effect does varying the value of the 𝑎 have on the values of the average
acceleration?
3. What effect does varying the value of 𝑏 have on the values of the average velocity?
4. What effect does varying the value of the 𝑏 have on the values of the average
acceleration?
Name: __________________________________
5. What effect does varying the value of 𝑐 have on the values of the average velocity?
6. What effect does varying the value of the 𝑐 have on the values of the average
acceleration?
7. Describe the graph of the average velocity. Why do you think the graph looks like
this?
8. Describe the graph of the average acceleration. Why do you think the graph looks like
this?
9. Did you expect the average acceleration to be constant? How is it related to Part 1?
Name: __________________________________
Excel Exploration Worksheet KEY:
You and your friend decide to take a road trip to North Carolina!
The plan is to drive in the car for 10 hours straight before taking a
break. The Excel spreadsheet tracked your position for the various
hours until you took your first break, along with your average
velocity and acceleration, and accompanying graphs of each are
provided.
Activity 1:
The spreadsheet is setup so you can change the values of the parameters for the slope and yintercept of a linear equation in the form 𝑦 = 𝑚𝑥 + 𝑏. Use the spreadsheet (Sheet 1) to answer
the following questions:
1. Using the linear equation, 𝑦 = 𝑚𝑥 + 𝑏, what does 𝑚 represent in this example? What
does 𝑏 represent?
𝑚 represents the velocity of the car and 𝑏 represents the initial position.
2. What effect does varying the value of the slope have on the values of the average
velocity?
As the slope increases, the average velocity is the same number.
3. What effect does varying the value of the slope have on the values of the average
acceleration?
No change. As the slope increases, average acceleration stays the same (stays
zero).
4. What effect does varying the value of the y-intercept have on the values of the average
velocity?
No change. As the y-intercept increases, the average velocity stays the same
(same value as slope).
5. What effect does varying the value of the y-intercept have on the values of the average
acceleration?
No change. As the y-intercept increases, the average acceleration stays the same
(stays zero).
6. In general, how do you calculate the average velocity?
Name: __________________________________
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒
7. In general, how do you calculate the average acceleration?
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒
8. Explain why the graph of the average velocity is a horizontal line. Would this be the case
for all linear equations? Why or why not.
The average velocity is a horizontal line because it is calculating the rate of
change in a linear equation, which is a constant value. Yes, this would be true for
all linear equations because the slope is constant.
9. Would you expect the graph of the average velocity to look the same for non-linear
functions? Why or why not.
No, because non-linear equations do not have a constant change. So, the average
velocity graph should look different.
10. Describe the graph of the average acceleration. Would this be the case for all linear
equations? Why or why not.
The graph of the average acceleration is a horizontal line at zero. Yes, this would
be the case for all linear equations because the rate of change for velocity is zero,
since the horizontal line has a slope of zero.
11. Would you expect the graph of the average acceleration to look the same for non-linear
functions? Why or why not.
No, since the graph of the average velocity would change for non-linear
equations, the average acceleration is the rate of change of velocity vs. time and
the average velocity would be different.
Name: __________________________________
Activity 2:
Repeat the above activity, but this time you are given a quadratic equation in the form 𝑦 =
𝑎𝑥 2 + 𝑏𝑥 + 𝑐. In this spreadsheet, you are able to change the values of the parameters for
𝑎, 𝑏, and 𝑐. Use the spreadsheet (Sheet 2) to answer the following questions:
1. What effect does varying the value of the 𝑎 have on the values of the average velocity?
As a changes (increases), the value of the average velocity change (increase).
2. What effect does varying the value of the 𝑎 have on the values of the average
acceleration?
As a changes, the values of the average acceleration change, but they are all the
same value for every position.
3. What effect does varying the value of 𝑏 have on the values of the average velocity?
As b changes, the values of the average velocity change.
4. What effect does varying the value of the 𝑏 have on the values of the average
acceleration?
As b changes, the values of the average acceleration remain the same.
5. What effect does varying the value of 𝑐 have on the values of the average velocity?
As c changes, the values of the average velocity remain the same.
6. What effect does varying the value of the 𝑐 have on the values of the average
acceleration?
As c changes, the values of the average acceleration remain the same.
7. Describe the graph of the average velocity. Why do you think the graph looks like this?
The graph of the average velocity is a line. So, it is a graph that looks represented
by a linear equation. The graph looks like a line because it is calculating the rate
of change for the position, which increases for constant value.
8. Describe the graph of the average acceleration. Why do you think the graph looks like
this?
The graph of the average acceleration is a horizontal line. This graphs is a
horizontal line because it is representing the rate of change for the average
velocity, which is a linear equation.
Name: __________________________________
9. Did you expect the average acceleration to be constant? How is it related to Part 1?
Answers may vary for the first question. (Hopefully they expected the average
acceleration to be constant)
The average acceleration is related to Part 1 because for a quadratic equation the
average acceleration is the same as the average velocity for the linear equation.
So, average velocity is always linear and average acceleration is always constant.