Answer
$$\frac{96}{125}$$
Work Step by Step
We find:
$\kappa=\frac{\left| y^{\prime \prime} x^{\prime}-y^{\prime} x^{\prime \prime}\right|}{\left(y^{\prime 2}+x^{\prime 2}\right)^{3 / 2}} $
$2 t=x^{\prime}(t), 2=x^{\prime \prime}(t)$
$\begin{array}{ll}3 t^{2}=y^{\prime}(t) & 6 t=y^{\prime \prime}(t) \\ 1=x^{\prime}(1 / 2)& 3 / 4=y^{\prime}(1 / 2) \quad 2=x^{\prime \prime}(1 / 2) \quad 3=y^{\prime \prime}(1 / 2)\end{array}$
$\frac{96}{125}=\kappa$
