Name: ____________________________
Linear Models
Date: ____________
Hr:_____
CBR Motion Graphs & Linear Equations
When you move toward or away from a location, your distance from that location at any time
can be plotted. In this activity, you will look for patterns about how changes in motion affect
the behavior of your graph.
Trial I: Away and Towards
Walker 1:
Walker 2:
Walk slowly and steadily AWAY from the motion detector at a constant rate.
Walk slowly and steadily TOWARDS the motion detector at a constant rate.
Sketch the resulting graphs for both Walkers below. Then answer the questions:
1. Why does the graph of Walker 1 go up, while the
graph of Walker 2 goes down?
2. What kind of equation would fit the graph of the two
walkers?
3. Estimate the slope and y-intercept of each graph
and write a possible equation for each walker below.
Show work as you estimate the slope:
Slope Calculations:
Walker 1:
Walker 2:
Equations:
Walker 1:
y = ______ x + _______
Walker 2:
y = ______ x + _______
4. Have the computer fit a linear equation through each walker and write the equations below:
Walker 1:
y = ______ x + _______
Walker 2:
y = ______ x + _______
5. Which Walker walked faster? Or did they walk the same speed? How do you know?
6. Which Walker started at a greater distance from the motion detector? How do you know?
7. The slope and y-intercept tell something about each walker. Explain their significance below. Use
units in your answers.
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Trial II: Standing Still
Walker 1:
Walker 2:
Stand motionless in front of the motion detector.
Create a line PARALLEL to that made by Walker 1.
8. What is the slope of Walker 1 and Walker 2 in this
case? Why?
9. Write a possible equation for each walker below.
No calculations should be necessary.
Walker 1:
y = ______ x + _______
y=
Walker 2:
y = ______ x + _______
y=
Trial III: Parallel Lines
Walker 1:
Walker 2:
Walk slowly and steadily AWAY from the motion detector at a constant rate.
Create a line PARALLEL to that made by Walker 1.
Sketch the resulting graphs for both Walkers below.
Then answer the questions:
10. What did Walker 2 have to do to create a line
PARALLEL to Walker 1?
11. Have the computer fit a linear equation through each
walker and write the equations below:
Walker 1:
y = ______ x + _______
Walker 2:
y = ______ x + _______
12. How can you use the equations to tell if the lines are PARALLEL?
13. Use your equations to predict the distance of both walkers if they kept walking for 25 seconds.
Show your work:
Walker 1:
Walker 2:
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Trial IV: Graph Matching
Each walker will try to match the three graphs below. Take turns trying until the match is as close as
possible. Explain the motion necessary to match each portion of the graph. Write your explanation on
the graph picture.
Walker 1:
Walker 2:
Summary:
14. For a walker that remains motionless, the slope value of the distance vs. time graph will be ______
15. When the walker heads AWAY from the motion detector, the slope value of the distance vs. time
graph will be ______________
16. When the walker heads TOWARDS the motion detector, the slope value of the distance vs. time
graph will be ______________
17. Faster walkers will have a _______________ slope than slower walkers.
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Assignment: Match each of the descriptions in the first column below with the appropriate graph
in the second column. Put the letter of the matching graph in the blank.
Descriptions:
Graphs:
Graph B:
Graph A:
____18. You start close to
the motion detector and
walk away at a steady
speed.
____19. You start far from
the motion detector and
walk towards it at a
medium speed, then walk
away from it going faster.
____20. You start far from
the motion detector and
walk towards it at a quick
speed, then walk away
from it going slower.
Graph C:
Graph D:
____21. You start far from
the motion detector and
walk towards it at a steady
speed.
____22. You start far from
the motion detector and
walk towards it at a steady
speed, then stop and stand
still.
Graph E:
Graph F:
____23. You start close to
the motion detector and
walk away at a steady
speed, then stop for awhile,
then walk back towards the
motion detector.
24. Write a short story or a description that could match the motion shown in the graph below. Be
sure to match all portions of the graph!!
Description:
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