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 $F _ { 0 }$ 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: (1) $\frac { 2 F _ { 0 } T } { M }$ (2) $\frac { F _ { 0 } T } { 2 M }$ (3) $\frac { 4 F _ { 0 } T } { 3 M }$ (4) $\frac { F _ { 0 } T } { 3 M }$
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 $F _ { 0 }$ 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:\\
(1) $\frac { 2 F _ { 0 } T } { M }$\\
(2) $\frac { F _ { 0 } T } { 2 M }$\\
(3) $\frac { 4 F _ { 0 } T } { 3 M }$\\
(4) $\frac { F _ { 0 } T } { 3 M }$