  The Brans-Dicke (BD) theory of gravity is taken as a possible theory of
k-essence coupled to gravity. It then has been realized that the BD scalar
field does indeed play a role of a k-essence, but in a very unique way which
distinguishes it from other k-essence fields studied in the literature. That
is, first in the BD scalar field-dominated era when the contribution from this
k-essence overwhelms those from other types of matter, the BD theory predicts
the emergence of a yet-unknown {\it zero acceleration} epoch which is an
intermediate stage acting as a ``crossing bridge'' between the decelerating
matter-dominated era and the accelerating phase. Upon realizing this, next,
closer study of the effects of this k-essence on the evolutionary behavior of
the matter-dominated and the accelerating eras has been performed. The result
of the study indicates that the BD scalar field appears to interpolate {\it
smoothly} between these two late-time stages by speeding up the expansion rate
of the matter-dominated era somewhat while slowing down that of the
accelerating phase to some degree. Thus with the newly found BD scalar
field-dominated era in between these two, the late-time of the universe
evolution appears to be mixed sequence of the three stages.
