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.
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