$($Section $14\mathrm{.}4)$ Let curve $C$ be described by vector function vec$(r)(t)=($:$cost,sint,2t^{\frac{3}{2}}$:$)$ on $0tb.$ Find the value$($s$)$ of $b$

so that the length of the curve on the given interval is $\frac{14}{27}$ units.