  We investigate the escape rate of an overdamped, self-propelled spherical
Brownian particle on a surface from a metastable potential well. Within a
modeling in terms of a 1D constant speed of the particle's active dynamics we
consider the associated rate using both numerical and analytical approaches.
Regarding the properties of the stationary state in the potential well, two
major timescales exist, each governing the translational and the rotational
dynamics of the particle, respectively. The particle radius is identified to
present the essential quantity in charge of regulating the ratio between those
timescales. For very small and very large particle radii, approximate analytic
expressions for the particle's escape rate can be derived, which, within their
respective range of validity, compare favorably with the precise escape
numerics of the underlying full two-dimensional Fokker-Planck description.
