A particle moving along $x$ -axis has acceleration $f$, at time $t$, given by $f = f _{0}\left(1-\frac{ t }{ T }\right)$, where $f _{0}$ and $T$ are constants. The particle at $t =0$ has zero velocity. In the time interval between $t =0$ and the instant when $f =0$, the particle's velocity $\left( v _{ x }\right)$ is: