A story about a bike ride, during which the rider decreased her speed.
A sketch of a graph describing the story.
A table containing quantitative information that can be gleaned from the story.
The figure also includes three other stories, which
can be described in graphs by performing horizontal or vertical reflections
on parts of the initial graph.
The axes of reflection pass through the point representing
the time and position at which the rider of the first story
decreased her speed.
position
time
f
g
speed
end position
end time
start position
start time
f
g
How are the quantities specified in story 1 expressed in the graph?
Use reflections to construct graphs that fit stories 2,3, and 4.
Record the sketch that corresponds to each story.
Examine the sketches you constructed and describe the
changes that occurred in the endpoints of the intervals making
up the graph and in the slopes of these intervals. Record
the data in the table that appears in the tool.
Use the Representing motion at several speeds tool
to check whether you can construct
a precise description of each story with the data you have and answer the questions that appear
in the story. Can answers to questions in one story help you find answers to questions
in the other stories?
