\documentclass[12pt]{article}
\usepackage{fullpage,amsmath,amsfonts,graphicx,url}

\def\d{{\mathrm d}}

\begin{document}

\title{General Mathematics and CPS II}
\author{Exercise 11}
\date{March 18, 2015}
\maketitle

\begin{enumerate}


\item Newton's second law of mechanics for a particle of mass $m$
situated at position $x(t)$ moving with velocity $v(t)$ and subject to
a force $F(x(t))$ can be written
\begin{gather*}
  \frac{\d x}{\d t} = v \,, \\
  m \, \frac{\d v}{\d t} = F(x(t)) \,.
\end{gather*}

Use the chain rule of calculus to show that the particle satisfies the
same equation with $t$ replaced by the reversed time $r=-t$ and $v$
replaced by $-v$.

\item Show that in a time-discrete, reversible, system with a finite
number of states any orbit must return to its initial state after a
finite number of steps.

\end{enumerate}
\end{document}
