  The random acceleration model is one of the simplest non-Markovian stochastic
systems and has been widely studied in connection with applications in physics
and mathematics. However, the occupation time and related properties are
non-trivial and not yet completely understood. In this paper we consider the
occupation time $T_+$ of the one-dimensional random acceleration model on the
positive half-axis. We calculate the first two moments of $T_+$ analytically
and also study the statistics of $T_+$ with Monte Carlo simulations. One goal
of our work was to ascertain whether the occupation time $T_+$ and the time
$T_m$ at which the maximum of the process is attained are statistically
equivalent. For regular Brownian motion the distributions of $T_+$ and $T_m$
coincide and are given by L\'evy's arcsine law. We show that for randomly
accelerated motion the distributions of $T_+$ and $T_m$ are quite similar but
not identical. This conclusion follows from the exact results for the moments
of the distributions and is also consistent with our Monte Carlo simulations.
