  We study the counting of level crossings for inertial random processes
exposed to stochastic resetting events. We develop the general approach of
stochastic resetting for inertial processes with sudden changes in the state
characterized by position and velocity. We obtain the level-crossing intensity
in terms of that of underlying reset-free process, for resetting events with
Poissonian statistics. We apply this result to the random acceleration process
and the inertial Brownian motion. In both cases, we show that there is an
optimal resetting rate that maximizes the crossing intensity, and we obtain the
asymptotic behavior of the crossing intensity for large and small resetting
rates. Finally, we discuss the stationary distribution and the mean
first-arrival time in the presence of resetting.
