The graph above represents a journey taken by a
group of bike riders who rode at a constant speed
for some time then increased their speed and continued
at a constant speed once more. The graph is schematic: it
gives a general description but does
not contain quantitative information about time intervals, distances,
or speeds.
The figure also presents various segments. Display them
and try to understand the meaning of the
length of each segment in terms of the
bicycle journey.
Among the many different journeys that the schematic graph
can describe are each of the three days of the camping trip taken
by the group of riders:
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Day 1
The ride lasted 3 hours.
During the first hour they rode at 15 kph, then increased
their speed to 20 kph.
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Day 2
The route was 99 km long. In the first 3 and a half hours they
rode at 18 kph, then increased their speed to 24 kph.
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Day 3
The route was 80 km long, and the ride lasted 6 hours.
At first they rode at 16 kph, then increased their speed to
20 kph.
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Construct descriptions of the rides
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The schematic graph can represent each of the rides above, but
more precise descriptions are needed to show the differences between
rides on different days.
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Present functions that describe the dependence of the
distance on time for each of the three days.
Use the Journeys in two parts and the
Representing motion at several speeds tools.
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For each of the three rides add details that do not appear in the
descriptions above.
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For the fourth day, the riders are planning a 90 km
route and want to complete it in 5 hours.
Propose several possible plans for a ride and
present them in graphs and in verbal descriptions.
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