  We constructed a sample of 23,344 radio-loud active galactic nuclei (RLAGN)
from the catalogue derived from the LOFAR Two-Metre Sky Survey (LoTSS) survey
of the HETDEX Spring field. Although separating AGN from star-forming galaxies
remains challenging, the combination of spectroscopic and photometric
techniques we used gives us one of the largest available samples of candidate
RLAGN. We used the sample, combined with recently developed analytical models,
to investigate the lifetime distribution of RLAGN. We show that large or giant
powerful RLAGN are probably the old tail of the general RLAGN population, but
that the low-luminosity RLAGN candidates in our sample, many of which have
sizes $<100$ kpc, either require a very different lifetime distribution or have
different jet physics from the more powerful objects. We then used analytical
models to develop a method of estimating jet kinetic powers for our candidate
objects and constructed a jet kinetic luminosity function based on these
estimates. These values can be compared to observational quantities, such as
the integrated radiative luminosity of groups and clusters, and to the
predictions from models of RLAGN feedback in galaxy formation and evolution. In
particular, we show that RLAGN in the local Universe are able to supply all the
energy required per comoving unit volume to counterbalance X-ray radiative
losses from groups and clusters and thus prevent the hot gas from cooling. Our
computation of the kinetic luminosity density of local RLAGN is in good
agreement with other recent observational estimates and with models of galaxy
formation.
