  Consider a particle which is randomly accelerated by Gaussian white noise on
the line segment $0<x<1$ and is absorbed as soon as it reaches $x=0$ or $x=1$.
The mean absorption time $T(x,v)$, where $x$ and $v$ denote the initial
position and velocity, was calculated exactly by Masoliver and Porr\`a in 1995.
We consider a more general boundary condition. On arriving at either boundary,
the particle is absorbed with probability $1-p$ and reflected with probability
$p$. The reflections are inelastic, with coefficient of restitution $r$. With
exact analytical and numerical methods and simulations, we study the mean
absorption time as a function of $p$ and $r$.
