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Cell[CellGroupData[{
Cell["Calculus: The Language of Change", "Title"],
Cell[TextData[{
StyleBox["Exercise Set 10.2\n",
FontVariations->{"Underline"->True}],
"Galileo's Law of Gravity"
}], "Subtitle"],
Cell["by John Robeson", "Subsubtitle"],
Cell[CellGroupData[{
Cell[TextData[{
StyleBox["Exercise 1) Galileo's Law and ", "Subtitle"],
Cell[BoxData[
\(\(d\^2\ s\)\/dt\^2\)]]
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Cell["\<\
Write Galileo's Law, \"The rate of increase in the speed of a falling body is \
constant\" in terms of the derivatives of the distance function s[t]. What \
derivative gives the speed? What derivative gives the rate at which the \
speed increases?\
\>", "Text"],
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Cell[TextData[{
"The rate of increase in the speed is the acceleration which is ",
Cell[BoxData[
\(\(d\^2\ s\)\/dt\^2\)]],
". For that to be constant means we can write the law as\n\n\t\t",
Cell[BoxData[
\(\(d\^2\ s\)\/dt\^2\)]],
" = g where g is a constant.\n\t\t\nIn other words if we measure the speed \
at any instant and then again one second later, the reading on our \
\"speedometer\" will have increased by an amount equal to g."
}], "Text"],
Cell[TextData[{
"The first derivative ",
Cell[BoxData[
\(ds\/dt\)]],
" gives us the falling speed."
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Cell[TextData[{
"The second derivative",
Cell[BoxData[
\(\(d\^2\ s\)\/dt\^2\)]],
" gives us the rate at which the falling speed increases."
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Cell[TextData[{
StyleBox["Exercise 2) Galileo's Law and the graph of ", "Subtitle"],
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\(ds\/dt\)]]
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Cell[TextData[{
"Galileo's Law is easiest to confirm with the data of the ",
StyleBox["Gravity",
FontWeight->"Bold"],
" program by looking at the graph of ",
Cell[BoxData[
\(ds\/dt\)]],
" (because error measurements are magnified each time we take differences \
of our data). What feature of the graph of velocity is equivalent to \
Galileo's Law?"
}], "Text"],
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Cell["Evaluate the cell below for a graph of velocity vs. time.", "Text"],
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AspectRatio \[Rule] 1, PlotRange \[Rule] {0, 100},
AxesLabel \[Rule] {time, velocity}]\), ";"}]], "Input"],
Cell["\<\
This graph is a staight line which means that the slope is constant which in \
turn means that the accelaeration is constant. So a linear graph of velocity \
is equivalent to Galileo's Law.\
\>", "Text"]
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}, Open ]]
}, Open ]]
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