  We study a tachyon model with non-minimal derivative coupling to gravity in
the Friedmann-Robertson-Walker flat cosmology. We propose the special
re-definition of the tachyon field which allows us to represent tachyon field
equation formally coinciding with its usual form but with re-defined Hubble
parameter. Two first integrals for the model equations are obtained that can
essentially simplify both further analysis and analytical solving for the
model. These integrals become the trivial identities in the case of minimal
coupling. The effective energy density and pressure of the tachyon field are
obtained, and the necessary condition of the possibility for this model to
expand with acceleration is derived.
