  We study front propagation in the reaction diffusion process
$\{A\stackrel{\epsilon}\to2A, A\stackrel {\epsilon_t}\to3A\}$ on a one
dimensional (1d) lattice with hard core interaction between the particles.
Using the leading particle picture, velocity of the front in the system is
computed using different approximate methods, which is in good agreement with
the simulation results. It is observed that in certain ranges of parameters,
the front velocity varies as a power law of $\epsilon_t$, which is well
captured by our approximate schemes. We also observe that the front dynamics
exhibits temporal velocity correlations and these must be taken care of in
order to find the exact estimates for the front diffusion coefficient. This
correlation changes sign depending upon the sign of $\epsilon_t-D$, where $D$
is the bare diffusion coefficient of $A$ particles. For $\epsilon_t=D$, the
leading particle and thus the front moves like an uncorrelated random walker,
which is explained through an exact analysis.
