  We study the nonequilibrium stationary state of a one-dimensional inertial
run-and-tumble particle (IRTP) trapped in a harmonic potential. We find that
the presence of inertia leads to two distinct dynamical scenarios, namely,
overdamped and underdamped, characterized by the relative strength of the
viscous and the trap time-scales. We also find that inertial nature of the
active dynamics leads to the particle being confined in specific regions of the
phase plane in the overdamped and underdamped cases, which we compute
analytically. Moreover, the interplay of the inertial and active time-scales
gives rise to several sub-regimes, which are characterized by very different
behaviour of position and velocity fluctuations of the IRTP. In particular, in
the underdamped regime, both the position and velocity undergoes transitions
from a novel multi-peaked structure in the strongly active limit to a single
peaked Gaussian-like distribution in the passive limit. On the other hand, in
the overdamped scenario, the position distribution shows a transition from a
U-shape to a dome-shape, as activity is decreased. Interestingly, the velocity
distribution in the overdamped scenario shows two transitions -- from a
single-peaked shape with an algebraic divergence at the origin in the strongly
active regime to a double peaked one in the moderately active regime to a
dome-shaped one in the passive regime.
