Answer
$$
\begin{aligned}
& \mathbf{v}_p=\{-1.60 \mathbf{i}\} \mathrm{m} / \mathrm{s} \\
& \mathbf{a}_p=\{-0.640 \mathbf{i}-12.0 \mathbf{j}-8.00 \mathbf{k}\} \mathrm{m} / \mathrm{s}^2
\end{aligned}
$$
Work Step by Step
$$
\begin{aligned}
\Omega= & \{5 \mathbf{k}-10 \mathbf{j}\} \mathrm{rad} / \mathrm{s} \\
\dot{\Omega}= & \{50 \mathbf{i}-4 \mathbf{j}+2 \mathbf{k}\} \mathrm{rad} / \mathrm{s}^2 \\
\mathbf{v}_P= & \Omega \times \mathbf{r}_P \\
\mathbf{v}_P & (5 \mathbf{k}-10 \mathbf{j} \times(160 \mathbf{j}+80 \mathbf{k}) \\
\mathbf{v}_P= & \{-1600 \mathbf{i}\} \mathrm{mm} / \mathrm{s} \\
= & \{-1.60 \mathbf{i}\} \mathrm{m} / \mathrm{s} \\
\mathbf{a}_P= & \Omega \times \mathbf{v}_P+\dot{\Omega} \times \mathbf{r}_P \\
\mathbf{a}_P= & \{50 \mathbf{i}-4 \mathbf{j}+2 \mathbf{k}\} \times(160 \mathbf{j}+80 \mathbf{k})+(-10 \mathbf{j}+5 \mathbf{k}) \times(-1600 \mathbf{i}) \\
\mathbf{a}_P= & \{-640 \mathbf{i}-12000 \mathbf{j}-8000 \mathbf{k}\} \mathrm{mm} / \mathrm{s}^2 \\
\mathbf{a}_P= & \{-0.640 \mathbf{i}-12.0 \mathbf{j}-8.00 \mathbf{k}\} \mathrm{m} / \mathrm{s}^2
\end{aligned}
$$
