1. **State the problem:** We are given the equation for displacement $$\vec{d} = \frac{(\vec{v}_f + \vec{v}_i)}{2} t$$ and values $$\vec{v}_f = 1.9\ \text{m/s}$$, $$t = 5.70\ \text{s}$$, and $$\vec{d} = 73.0\ \text{m}$$. We need to solve for the initial velocity $$\vec{v}_i$$. 2. **Write the formula and isolate $$\vec{v}_i$$:** $$\vec{d} = \frac{(\vec{v}_f + \vec{v}_i)}{2} t$$ Multiply both sides by 2: $$2\vec{d} = (\vec{v}_f + \vec{v}_i) t$$ Divide both sides by $$t$$: $$\frac{2\vec{d}}{t} = \vec{v}_f + \vec{v}_i$$ Subtract $$\vec{v}_f$$ from both sides: $$\vec{v}_i = \frac{2\vec{d}}{t} - \vec{v}_f$$ 3. **Plug in the known values:** $$\vec{v}_i = \frac{2 \times 73.0}{5.70} - 1.9$$ 4. **Calculate:** $$\frac{146.0}{5.70} = 25.6140...$$ So, $$\vec{v}_i = 25.6140 - 1.9 = 23.7140\ \text{m/s}$$ 5. **Final answer:** $$\boxed{\vec{v}_i = 23.7\ \text{m/s}}$$ (rounded to 3 significant figures)