A $2-$kg particle has a time$-$dependent velocity ofThe particle is at the origin of the coordinate system at t $=0.$ Determine $($a$)$ the position vector of the particle, $($b$)$ the acceleration of the particle, $($c$)$ the kinetic energy of the particle at t $=1$ s$,$ and $($d$)$ the linear momentum of the particle at t $=1$ s$.$