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Cell["Calculus: The Language of Change", "Title"],
Cell[TextData[{
StyleBox["Exercise Set 10.1\n",
FontVariations->{"Underline"->True}],
"Acceleration"
}], "Subtitle"],
Cell["by John Robeson", "Subsubtitle"],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Exercise 1) 9.2.1 Again", "Subtitle"]], "Subtitle"],
Cell[TextData[{
"The first exercise seeks your everyday interpretation of the positive and \
negative signs of ",
Cell[BoxData[
\(ds\/dt\)]],
"and ",
Cell[BoxData[
\(\(d\^2\ s\)\/dt\^2\)]],
" on the hypothetical trip from \nExercise 9.2.1. We need to understand \
the mechanical interpretation of these derivatives as well as their graphical \
interpretation."
}], "Text"],
Cell[TextData[{
"Look up your old solution to Exercise 9.2.1 and add a graphing table like \
the ones from Chapter 9 with slope and bending. Fill in the parts of the \
table corresponding to ",
Cell[BoxData[
\(ds\/dt\)]],
" and ",
Cell[BoxData[
\(\(d\^2\ s\)\/dt\^2\)]],
" using the microscopic slope and smile and frown icons including + and - \
signs. Remember that ",
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\(\(d\^2\ s\)\/dt\^2\)]],
" is the derivative of the function ",
Cell[BoxData[
\(ds\/dt\)]],
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"(a) Where is your speed increasing? Decreasing? Zero? If speed is \
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(The graph of v[t] has upward slope and positive derivative, ",
Cell[BoxData[
\(dv\/dt\)]],
" = ",
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\(\(d\^2\ s\)\/dt\^2\)]],
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"Here is one solution.\n\nt(min)\t0\t2\t8\t10\t10.5\t12.5\t24.5\t26\t104\t\
105.5\t111.5\t113.5\t114\t120\n\ns(mi.)\t0\t0.5\t3\t3.5\t3.5\t4\t9\t10\t94.5\t\
95.5\t98\t98.5\t98.5\t100\n\ns'\t \[UpperRightArrow]\t \
\[UpperRightArrow]\t \[UpperRightArrow]\t \[RightArrow]\t \
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\[UpperRightArrow]\t \[RightArrow]\t \[UpperRightArrow]\n\ns''\t \
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"(a) Where is your speed increasing? Decreasing? Zero? If speed is \
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(The graph of v[t] has upward slope and positive derivative, ",
Cell[BoxData[
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" affects the graph of s[t].)"
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Cell["\<\
Our speed is increasing in segments 1, 5, 7, 13 which is whenever s'' has a \
smile entry. It is decreasing in segments 3, 9, 11, 13 which is when s'' has \
a frown entry. The speed is zero when we are stopped during segments 4 and \
12.\
\>", "Text"],
Cell["\<\
So when speed is increasing our graph of s[t] is smile shaped.\
\>", "Text"]
}, Open ]]
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"(b) Is ",
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Cell[CellGroupData[{
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"Compute the average speeds corresponding to the positions in Table 10.4 \
and write them next to the correct midpoint times so that they correspond to \
continuous velocities at those times. Then use your velocities to compute \
accelerations at the proper times. Simply fill in the places where the \
question marks appear in the velocity and acceleration Tables 10,5 and 10.6. \
The data are also contained in the ",
StyleBox["Gravity",
FontWeight->"Bold"],
" program so you can complete this arithmetic with the computer in Exercise \
10.2.2."
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Observe that the acceleration is essentially constant at 9.8.
\
\>", "Text"]
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