(a) To find the velocity, integrate the acceleration:

\(v = \int 0.1t^{3/2} \, dt = 0.04t^{5/2} + 1.72\)

Set \(v = 3\) and solve for \(t\):

\(0.04t^{5/2} + 1.72 = 3\)

\(0.04t^{5/2} = 1.28\)

\(t^{5/2} = 32\)

\(t = 4\)

(b) To find the displacement, integrate the velocity:

\(s = \int (0.04t^{5/2} + 1.72) \, dt\)

\(s = \left[ \frac{2}{175}t^{7/2} + 1.72t \right]\)

Evaluate from \(t = 0\) to \(t = 2\):

\(s = \left[ \frac{2}{175}(2)^{7/2} + 1.72(2) \right]\)

\(s = 3.57 \text{ m}\)