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 \( F = F_{0} \left[ 1 - \left( \dfrac{t -T}{T} \right)^{2} \right] \). Where \( F_{0} \) and \( T \) are constants. The force acts only for the time interval \( 2T \). The velocity \( v \) of the particle after time \( 2T \) is:
