In this paper, we have investigated late time acceleration for a spatially flat dust filled Universe in Brans-Dicke theory in the presence of a positive cosmological constant $Lambda$ . Expressions for Hubbles constant, luminosity distance and apparent magnitude have been obtained for our model. The theoretical results are compared with the observed values of the the latest 287 high red shift ($ .3 leq z leq 1.4$ ) SN Ia supernova datas taken from Union 2.1 compilation to estimate the present values of the matter and dark energy parameters $(Omega_{m})_0$ and $(Omega_{Lambda})_0$. We have also estimated the present value of Hubbles constant $H_0$ in the light of a updated sample of Hubble parameter measurements including 19 independent data points. The results are found to be in good agreement with recent astrophysical observations. We have also calculated various physical parameters such as the matter and dark energy densities, the present age of the universe and deceleration parameter. The value for BD-coupling constant $omega$ is set to be 40000 on the basis of accuracy of the solar system tests and recent experimental evidence.
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