We study the kinematics of the M87 jet using the first year data of the KVN and VERA Array (KaVA) large program, which has densely monitored the jet at 22 and 43 GHz since 2016. We find that the apparent jet speeds generally increase from $approx0.3c$ at $approx0.5$ mas from the jet base to $approx2.7c$ at $approx20$ mas, indicating that the jet is accelerated from subluminal to superluminal speeds on these scales. We perform a complementary jet kinematic analysis by using archival Very Long Baseline Array monitoring data observed in $2005-2009$ at 1.7 GHz and find that the jet is moving at relativistic speeds up to $approx5.8c$ at distances of $200-410$ mas. We combine the two kinematic results and find that the jet is gradually accelerated over a broad distance range that coincides with the jet collimation zone, implying that conversion of Poynting flux to kinetic energy flux takes place. If the jet emission consists of a single streamline, the observed trend of jet acceleration ($Gammapropto z^{0.16pm0.01}$) is relatively slow compared to models of a highly magnetized jet. This indicates that Poynting flux conversion through the differential collimation of poloidal magnetic fields may be less efficient than expected. However, we find a non-negligible dispersion in the observed speeds for a given jet distance, making it difficult to describe the jet velocity field with a single power-law acceleration function. We discuss the possibility that the jet emission consists of multiple streamlines following different acceleration profiles, resulting in jet velocity stratification.
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