  We study the dispersion relations of mesons in a particular hot strongly
coupled supersymmetric gauge theory plasma. We find that at large momentum k
the dispersion relations become omega = v_0 k + a + b/k + ..., where the
limiting velocity v_0 is the same for mesons with any quantum numbers and
depends only on the ratio of the temperature to the quark mass T/m_q. We
compute a and b in terms of the meson quantum numbers and T/m_q. The limiting
meson velocity v_0 becomes much smaller than the speed of light at temperatures
below but close to T_diss, the temperature above which no meson bound states at
rest in the plasma are found. From our result for v_0, we find that the
temperature above which no meson bound states with velocity v exist is
T_diss(v) \simeq (1-v^2)^(1/4) T_diss, up to few percent corrections.We thus
confirm by direct calculation of meson dispersion relations a result inferred
indirectly in previous work via analysis of the screening length between a
static quark and antiquark in a moving plasma. Although we do not do our
calculations in QCD, we argue that the qualitative features of the dispersion
relation we compute, including in particular the relation between dissociation
temperature and meson velocity, may apply to bottomonium and charmonium mesons
propagating in the strongly coupled plasma of QCD. We discuss how our results
can contribute to understanding quarkonium physics in heavy ion collisions.
