(a) Use the constant acceleration equations to find expressions for \(s_{AB}\) and \(s_{BC}\):

\(s_{AB} = 2 \times 4.5 - \frac{1}{2} a \times 2^2\)

\(s_{BC} = 2 \times 4.5 + \frac{1}{2} a \times 2^2\)

Given \(s_{AB} = \frac{4}{5} s_{BC}\), substitute:

\([2 \times 4.5 - \frac{1}{2} a \times 2^2] = \frac{4}{5} [2 \times 4.5 + \frac{1}{2} a \times 2^2]\)

Solve for \(a\):

\(a = 0.5 \text{ m s}^{-2}\)

(b) Find \(AC\):

\(s_{AB} = 8 \text{ m}\) and \(s_{BC} = 10 \text{ m}\)

\(s_{AC} = s_{AB} + s_{BC} = 8 + 10 = 18 \text{ m}\)