\((i) To find the displacement of P from O when t = 10, we use the formula for displacement with constant acceleration:\)

\(s = \frac{(u + v)}{2} \times t\)

where \(u = 1.5\) m/s, \(v = 3.5\) m/s, and \(t = 10\) s.

\(s = \frac{(1.5 + 3.5)}{2} \times 10 = 25 \text{ m}\)

(ii) For particle Q, the acceleration is given by \(a = 0.03t\). To find the velocity, integrate the acceleration:

\(v = \int 0.03t \, dt = 0.015t^2 + C\)

Given that \(v = 3.5\) m/s when \(t = 10\), we find \(C\):

\(3.5 = 0.015 \times 100 + C\)

\(3.5 = 1.5 + C\)

\(C = 2\)

Thus, the velocity equation is \(v = 0.015t^2 + 2\).

To find the displacement, integrate the velocity:

\(s = \int (0.015t^2 + 2) \, dt = 0.005t^3 + 2t + D\)

Since Q starts from O, \(D = 0\).

At \(t = 10\):

\(s = 0.005 \times 1000 + 20 = 5 + 20 = 25 \text{ m}\)

Therefore, the displacement of Q is also 25 m, the same as P.