1. The problem asks to find the instantaneous velocity $v(t_0)$ for the function $s(t)$ at the given time $t_0$. 2. The instantaneous velocity is the derivative of the position function $s(t)$ with respect to time $t$, evaluated at $t = t_0$: $$v(t_0) = s'(t_0) = \left. \frac{ds}{dt} \right|_{t=t_0}$$ 3. For part (a), the position function is: $$s = 3 \ln t - 3t + 2$$ 4. Differentiate $s$ with respect to $t$: $$s'(t) = \frac{d}{dt} (3 \ln t) - \frac{d}{dt} (3t) + \frac{d}{dt} (2) = \frac{3}{t} - 3 + 0 = \frac{3}{t} - 3$$ 5. Evaluate the derivative at $t_0 = 1$: $$v(1) = \frac{3}{1} - 3 = 3 - 3 = 0$$ 6. Therefore, the instantaneous velocity at $t_0=1$ is $0$. This means at time $t=1$, the object is momentarily at rest. Final answer: $$\boxed{v(1) = 0}$$