  The present paper reports a study on the dimensionless parameter $\omega$ in
Brans-Dicke theory. Based on a particular choice of scale factor $a$, we have
investigated the signature flip of the deceleration parameter $q$ to see
whether the transition from decelerated to accelerated expansion of the
universe is achievable under this choice of scale factor. Restrictions on the
parameters obtained for this choice of scale factor have been subsequently used
for discussing the Brans-Dicke parameter for two choices of scalar fields
$\phi$. Moreover, analytical solutions for the Brans-Dicke parameter without
any assumption about the scalar field have been obtained from the modified
field equations through the choice of scale factor under consideration. Viable
models have been obtained by comparing the results with observations.
