We describe a study of the side-to-side asymmetries on kpc scales in the je
ts of FR I radio galaxies selected from the B2 sample. The basic data are j
et surface brightnesses and widths determined by fitting transverse profile
s to Very Large Array (VLA) images at a range of distances from the core. D
ifferences between the jets at a given distance from the nucleus are interp
reted as effects of Doppler beaming on intrinsically symmetrical flows and
are compared with the model derived for 3C31 by Laing & Bridle and with sim
pler variants. The jet/counterjet brightness ratios where the main jet firs
t brightens are correlated with core prominence, as expected for a relativi
stic flow. From the distribution of brightness ratios, we infer that jets h
ave a maximum velocity approximate to 0.9c where they first flare and brigh
ten, but there is also evidence for additional slower material. Deceleratio
n to subrelativistic speeds occurs on scales which increase with radio powe
r. Jets in the majority of sources with luminosities < 10(24)WHz(-1) at 1,4
GHz become essentially symmetrical land therefore subrelativistic) within
2 kpc of the core. In more powerful sources, jets that flare within the fir
st 2 kpc become symmetrical by 10 kpc, but a subset of the most luminous ob
jects has jets which remain asymmetrical to larger distances. The point at
which the brighter jet flares appears to correspond to a sudden increase in
rest-frame emissivity, but the ratio of distances to the flaring point in
main and counterjets is anticorrelated with brightness ratio, as expected f
or a decelerating relativistic flow. Brightness and full width at half-maxi
mum (FWHM) ratios are also anticorrelated, an effect which we interpret as
a result of Doppler beaming for a flow in which the velocity decreases radi
ally outwards from the jet axis. Jet deceleration by entrainment of externa
l material provides a natural explanation for these velocity gradients. The
jet energy flux is roughly consistent with energy supply to the lobes over
a source lifetime estimated from spectral index measurements. Our results
are qualitatively consistent with unified models of FR I radio galaxies and
BL Lac objects, but require some modifications to the standard picture.