A particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F\, = \,{F_0}\left[ {1 - {{\left( {\frac{{t - T}}{T}} \right)}^2}} \right]$ where, ${F_0}\,\,{\rm{and}}\,\,T$ are constants. The force acts only for the time interval $2\,T$ . The velocity $v$ of the particle after time $2\,T$ is