Motion at changing speeds
Stopping a train
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In several European countries, as well as in Japan,
super-fast trains travel at speeds
of 250-300 km/hour. Building such a train involves
many technological challenges; one
of them is a braking system that allows the trains,
weighing hundreds or thousands of tons, to stop.
These super-fast trains are controlled by a computerized
system.
You will now perform a mathematical
analysis of the braking process of a train
to help the engineers program the
computer that controls the train.
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The graphs shows the braking process of
a super-fast train travelling at 300 km/hour before
braking begins. In standard braking (stopping at stations), the
train stops after 3 minutes; if the emergenency brakes
are used, the train stops after a minute and a half.
Analyze the braking process to help the
designers answer the following questions:
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velocity
(km/hour) |
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time (minutes) |
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At what distance from a train station should the brakes
to be applied in order to reach a complete stop at the station?
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If the mechanic detects a hazard ahead, for example a car stuck
on the tracks, what are the conditions necessary for the train to come to a
complete stop before reaching the car?
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Construct mathematical descriptions of braking processes
Construct a description
(using, for example, graphs, value tables, and
correspondence rules) of the train's braking process
during standard and emergency braking.
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Use your descriptions to answer the questions
raised by the designers as well as
other questions you may raise.
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Describe your considerations and decisions. Discuss the
level of accuracy of your results.
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