The probability that a randomly accelerated particle in two dimensions has
not yet left a simply connected domain A after a time t decays as e(-E0t) f
or long times. The same quantity E-0 also determines the confinement free e
nergy per unit length Deltaf = k(B)T E-0 of a semiflexible polymer in a nar
row cylindrical pore with cross section A. From simulations of a randomly a
ccelerated particle we estimate the universal amplitude of Deltaf for both
circular and rectangular cross sections.