= Solution
Rewrite the complex <position> as $z(t)=2+3i/(t-i)$. Differentiating gives the complex <velocity> and <acceleration>
$$
\dot z=-\frac{3i}{(t-i)^2},\qquad
\ddot z=\frac{6i}{(t-i)^3}.
$$
For real $t$, $|t-i|=\sqrt{t^2+1}$. Their requested magnitudes are therefore
$$
\boxed{|\dot z|=\frac3{t^2+1},\qquad
|\ddot z|=\frac6{(t^2+1)^{3/2}}.}
$$
There is no pole for real time. The magnitude is the Euclidean length of the two Cartesian components, not the modulus of either component separately.
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