  We compute exactly the mean perimeter <L(T)> and the mean area <A(T)> of the
convex hull of a random acceleration process of duration T in two dimensions.
We use an exact mapping that relates, via Cauchy's formulae, the computation of
the perimeter and the area of the convex hull of an arbitrary two dimensional
stochastic process [x(t); y(t)] to the computation of the extreme value
statistics of the associated one dimensional component process x(t). The latter
can be computed exactly for the one dimensional random acceleration process
even though the process in non-Markovian. Physically, our results are relevant
in describing theaverage shape of a semi-flexible ideal polymer chain in two
dimensions.
