(i) To find when P is at instantaneous rest, set the velocity v to zero:

\(4t^2 - 8t + 3 = 0\)

Factor the quadratic equation:

\((2t - 3)(2t - 1) = 0\)

Solving gives \(t = 0.5\) and \(t = 1.5\).

(ii) To find the distance travelled, integrate the velocity function:

\(s = -\int (4t^2 - 8t + 3) \, dt\)

Integrate to find the displacement:

\(s = -\left[ \frac{4}{3}t^3 - 4t^2 + 3t \right]_{0.5}^{1.5}\)

Evaluate the definite integral:

\(s = -\left[ \left( \frac{4}{3}(1.5)^3 - 4(1.5)^2 + 3(1.5) \right) - \left( \frac{4}{3}(0.5)^3 - 4(0.5)^2 + 3(0.5) \right) \right]\)

\(s = -\left[ 0 - \left( -\frac{2}{3} \right) \right] = \frac{2}{3}\) m