Motion at changing speeds
Accelerating and decelerating
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This task involves planning the ride of a subway train
as it travels from one station to the next. In the first
part of the ride, the train gradually accelerates; in the second part
it gradually slows down until it comes to a halt at the next station.
Below is a time-velocity graph describing such a ride.
The rate of acceleration is usually lower than the rate
of deceleration. Consider a subway train with the
following characterisrics:
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velocity increases by 0.2 meters/second every second
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acceleration
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velocity decreases by 1 meter/second every second
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deceleration
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A computerized system drives the train between stations,
so that the driver can dispatch the train to the next station
by pressing a button. To plan such a system, the computer
must know at which point in the ride to stop accelerating and
apply the brakes to start decelerating.
Suppose that the distance between two stations is 1
kilometer.
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Plan the train ride
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Construct functions describing the dependence
of velocity and position on time. Plan
the ride so that it starts from standstill
in one station and stops at the next one.
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How long will it take the train
to go from one station to the next?
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What will be the maximum speed
during the ride?
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Use the
Functions on intervals tool from the general tools list to present a function describing
the dependence of velocity on time, and a function describing
the dependence of position on time.
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