Since a weight of 8 lbs has a mass of $8\/32 \=1\/4$ slug, Newton's second law $\mathbf{F}\=m \mathbf{a}\=m \stackrel{..}{\mathbf{R}}$ gives

$\stackrel{..}{\mathbf{R}}\=\mathbf{F}\/m$ = 4$\left[\begin{array}{c}1\\ -2\end{array}\right]\=\left[\begin{array}{c}4\\ -8\end{array}\right]$

Now $\stackrel{\.}{v}\=\stackrel{..}{\mathbf{R}}·\mathbf{T}$ = $\left[\begin{array}{c}4\\ -8\end{array}\right]·\left[\begin{array}{c}1\\ 0\end{array}\right]$ = 4 and $\mathrm{\κ} v^2\=\stackrel{..}{\mathbf{R}}·\mathbf{N}$ = $\left[\begin{array}{c}4\\ -8\end{array}\right]·\left[\begin{array}{c}0\\ -1\end{array}\right]\=8$, so $v^2\=4$ and $v\=2$. (The speed $v$ is the norm of $\stackrel{\.}{\mathbf{R}}$, so is necessarily positive.)