  We report the effect of field, temperature and thermal history on the time
dependence in resistivity and magnetization in the phase separated state of Al
doped Pr$_{0.5}$Ca$_{0.5}$MnO$_3$. The rate of time dependence in resistivity
is much higher than that of magnetization and it exhibits a different cooling
field dependence due to percolation effects. Our analysis show that the time
dependence in physical properties depends on the phase transition dynamics
which can be effectively tuned by variation of temperature, cooling field and
metastable phase fraction. The phase transition dynamics can be broadly divided
into the arrested and un-arrested regimes, and in the arrested regime, this
dynamics is mainly determined by time taken in the growth of critical nuclei.
An increase in cooling field and/or temperature shifts this dynamics from
arrested to un-arrested regime, and in this regime, this dynamics is determined
by thermodynamically allowed rate of formation of critical nuclei which in turn
depends on the cooling field and available metastable phase fraction. At a
given temperature, a decrease in metastable phase fraction shifts the crossover
from arrested to un-arrested regimes towards lower cooling field. It is rather
significant that inspite of the metastable phase fraction calculated from
resistivity being somewhat off from that of magnetization, their cooling field
dependence exhibits a striking similarity which indicate that the dynamics in
arrested and un-arrested regimes are so different that it comes out vividly
provided that the measurements are done around percolation threshold.
