Problem $4.$ Suppose that the acceleration vector of a vector$-$valued function vec$(r)(t)$ is given by vec$(a)(t)=cos(tvec(k)).$ Suppose that at $t=0,$ the velocity vector and the position vector have values vec$(v)(0)=$vec$(i)-$vec$(j),$ and vec$(r)(0)=$vec$(i).$ Find vec$(r)(t)$ and vec$(v)(t).$