To solve this problem, we need to find the velocity and acceleration of the particle by differentiating the displacement function.

The displacement function is given by \(s = 2t^2 - \frac{80}{3}t^{3/2}\).

(i) First, find the velocity \(v\) by differentiating \(s\) with respect to \(t\):

\(v = \frac{ds}{dt} = \frac{d}{dt}(2t^2 - \frac{80}{3}t^{3/2}) = 4t - 40t^{1/2}\).

Next, find the acceleration \(a\) by differentiating \(v\) with respect to \(t\):

\(a = \frac{dv}{dt} = \frac{d}{dt}(4t - 40t^{1/2}) = 4 - 20t^{-1/2}\).

Set the acceleration to zero to find the time:

\(4 - 20t^{-1/2} = 0\)

\(4 = 20t^{-1/2}\)

\(t^{-1/2} = \frac{1}{5}\)

\(t^{1/2} = 5\)

\(t = 25\) s

(ii) Substitute \(t = 25\) into the displacement and velocity equations:

Displacement: \(s = 2(25)^2 - \frac{80}{3}(25)^{3/2}\)

\(s = 2(625) - \frac{80}{3}(125)\)

\(s = 1250 - \frac{10000}{3}\)

\(s = 1250 - 3333.33\)

\(s = -2083.3\) m

Velocity: \(v = 4(25) - 40(25)^{1/2}\)

\(v = 100 - 40(5)\)

\(v = 100 - 200\)

\(v = -100\) m/s