  An LRS Bianchi I model is considered with constant deceleration parameter,
$q=\alpha-1$, where $\alpha\geq0$ is a constant. The physical and kinematical
behaviour of the models for $\alpha=0$ and $\alpha\neq0$ is studied in detail.
The model with $\alpha=0$ describes late time acceleration, but eternal
inflation demands a violation of the NEC and WEC. The acceleration is caused by
phantom matter which approaches a cosmological constant at late times. The
solutions with a scalar field also show that the model is compatible with a
phantom field only. A comparison with the observational outcomes indicates that
the universe has entered into the present accelerating phase in recent past
somewhere between $0.2\lesssim z\lesssim0.5$. The model obeys the "cosmic no
hair conjecture". The models with $0<\alpha<1$ describe late time acceleration
driven by quintessence dark energy. A violation of the NEC and WEC is required
to accommodate the early inflationary epoch caused by phantom matter. The
models with $1<\alpha<3$ describe decelerating phases which are usually occur
in the presence of dust or radiation. These models are also found anisotropic
at early times and attain isotropy at late times. The model for $\alpha=3$
represents a stiff matter era which also has shear at early stages and becomes
shear free at late times, but it evolves with an insignificant ceaseless
anisotropy. The models with $\alpha>3$ violate the DEC and the corresponding
scalar field models have negative potential which is physically unrealistic.
