The curve \(C\) has parametric equations
\(x=\frac{2}{3} t^{\frac{3}{2}}-2 t^{\frac{1}{2}}, \quad y=2 t+5, \quad \text { for } 0\lt t \leqslant 3 .\)
(a) Find the exact length of \(C\).
(b) Find the set of values of \(t\) for which \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\gt 0\).