Inertial dynamics of run-and-tumble particle

We study the dynamics of a single inertial run-and-tumble particle on a straight line. The motion of this particle is characterized by two intrinsic timescales, namely, an inertial and an active timescale. We show that interplay of these two times-scales leads to the emergence of four distinct regimes, characterized by different dynamical behavior of mean-squared displacement and survival probability. We analytically compute the position distributions in these regimes when the two timescales are well separated. We show that in the large-time limit, the distribution has a large deviation form and compute the corresponding large deviation function analytically. We also find the persistence exponents in the different regimes theoretically. All our results are supported with numerical simulations.