%% LyX 1.1 created this file.  For more info, see http://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
\documentclass[11pt,oneside]{amsart}
\usepackage[T1]{fontenc}
\usepackage{geometry}
\geometry{verbose,letterpaper,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\setlength\parskip{\medskipamount}
\setlength\parindent{0pt}

\makeatletter


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
\providecommand{\LyX}{L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\@}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
 \theoremstyle{plain}    
 \newtheorem{thm}{Theorem}[section]
 \numberwithin{equation}{section} %% Comment out for sequentially-numbered
 \numberwithin{figure}{section} %% Comment out for sequentially-numbered
 \theoremstyle{definition}
  \newtheorem{example}[thm]{Example}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
\setcounter{section}{2}
\setcounter{subsection}{3}

\makeatother

\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\subsection{Applications of the derivative.}

\begin{example}
If the position of a particle (in meters, along a line) is given by \( s=t^{3}-4.5t^{2}-7t \),
for \( t\geq 0 \), find the velocity \( v(t) \), and find when the velocity
reaches \( 5\, m/sec \). What motion did the particle have at \( t=0 \)?
\end{example}

\subsubsection*{Solution:}

The velocity is \( v(t)=3t^{2}-9t-7 \), so, at \( t=0 \) the velocity was
\( -7 \), meaning that the particle was going backwards at \( 7\, m/sec \).
The velocity was \( 5 \) when \begin{eqnarray*}
5 & = & 3t^{2}-9t-7,\, \mathrm{or}\\
0 & = & 3t^{2}-9t-12\\
 & = & (3t+12)(t-1).
\end{eqnarray*}
Now, we presume that time is going forward, so we will not count the solution
\( t=-4 \), so the answer will be \( t=1 \) only. 
\end{document}
