(i) To find the time taken for the motorcyclist to travel from A to B, we set the velocity equation to zero:

\(v = t - 0.01t^2 = 0\)

Solving for t, we get:

\(t(1 - 0.01t) = 0\)

\(Thus, t = 0 or t = 100. Since the motorcyclist starts at t = 0, the time taken is t = 100 seconds.\)

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

\(\int v \, dt = \int (t - 0.01t^2) \, dt\)

This gives:

\(\frac{t^2}{2} - \frac{0.01t^3}{3}\)

\(Evaluating from t = 0 to t = 100:\)

\(\left( \frac{100^2}{2} - \frac{0.01 \times 100^3}{3} \right) - \left( \frac{0^2}{2} - \frac{0.01 \times 0^3}{3} \right)\)

Calculating this gives:

\(5000 - \frac{100000}{3} = 1670 \text{ m}\)