  The formation and dynamics of coronal rain are currently not fully
understood. Coronal rain is the fall of cool and dense blobs formed by thermal
instability in the solar corona towards the solar surface with acceleration
smaller than gravitational free fall. We aim to study the observational
evidence of the formation of coronal rain and to trace the detailed dynamics of
individual blobs. We used time series of the 171 \AA\, and 304 \AA\, spectral
lines obtained by the Atmospheric Imaging Assembly (AIA) on board the Solar
Dynamic Observatory (SDO) above active region AR 11420 on February 22, 2012.
Observations show that a coronal loop disappeared in the 171 \AA\ channel and
appeared in the 304 \AA\ line$\text{}\text{}$ more than one hour later, which
indicates a rapid cooling of the coronal loop from 1 MK to 0.05 MK. An energy
estimation shows that the radiation is higher than the heat input, which
indicates so-called catastrophic cooling. The cooling was accompanied by the
formation of coronal rain in the form of falling cold plasma. We studied two
different sequences of falling blobs. The first sequence includes three
different blobs. The mean velocities of the blobs were estimated to be 50 km
s$^{-1}$, 60 km s$^{-1}$ and 40 km s$^{-1}$. A polynomial fit shows the
different values of the acceleration for different blobs, which are lower than
free-fall in the solar corona. The first and second blob move along the same
path, but with and without acceleration, respectively. We performed simple
numerical simulations for two consecutive blobs, which show that the second
blob moves in a medium that is modified by the passage of the first blob.
Therefore, the second blob has a relatively high speed and no acceleration, as
is shown by observations. The second sequence includes two different blobs with
mean velocities of 100 km s$^{-1}$ and 90 km s$^{-1}$, respectively.
