A particle of mass \(m=1 \mathrm{~kg}\) moves in the \(x y\)-plane. The force on it at time \(t\) is \(F(t)=[2 \sin (\alpha t) \hat{\mathbf{i}}+3 \cos (\alpha t) \hat{\mathbf{j}}] \mathrm{N}\), where \(\alpha=1 \mathrm{~s}^{-1}\). At time \(t=0\), the particle is at rest at the origin. Calculate the magnitude of its position vector \(\mathbf{r}\) (in \(\mathrm{m}\) ) and velcoity vector \(\mathbf{v}\) (in \(\mathrm{m} / \mathrm{s}\) ) at time \(t=\frac{\pi}{2} \mathrm{~s}\).

1. A \(r=\sqrt{\left[(\pi-2)^2+9\right]}, v=\sqrt{13}\)
2. B \(r=\sqrt{13}, v=\sqrt{9}\)
3. C \(r=\sqrt{3}, v=\sqrt{2}\)
4. D None of these