  In this paper, we derive maximal acceleration of a massive particle in
Rainbow gravity. Using eight-dimensional phase-space metric compatible with
Rainbow gravity, we obtain the maximal acceleration, valid up to first order in
the Rainbow gravity parameter $\eta$. Using the positivity condition on maximal
acceleration, we find the upper bound on the Rainbow gravity parameter is of
the order of $~10^{22}$ for positron and $10^{-44}$ for a black hole. After
obtaining the expression for maximal acceleration for different choices of
Rainbow functions, we derive corresponding modifications to Unruh temperature.
Comparing with the observational value of the Unruh temperature, we find the
upper bound on $\eta$ as $~10^{32}$ for positron radiation. %and of the order
of $10^{-100}$ for radiation from a black hole. We then derive geodesic
equations for different choices of Rainbow functions and also obtain Newtonian
limit of these geodesic equations. We find that the changes in the value of
maximum acceleration, maximum temperature and Newtonian force equation are
dependent on the choices of Rainbow functions.
