Curvature in Three Dimensions

Define Parametric Curve

x[t_]:=2+t^2; y[t_]:=t^2-4*t;
z[t_]:=2*t;

Plot Space Curve

ParametricPlot3D[{x[t],y[t],z[t]},{t,-5,5}, ColorFunction->Hue, PlotStyle->{Thick}, AxesLabel->{"x","y","z"}]

Define Kappa(t) For Curve

kap[t_]:=5/(4*(2*t^2-4*t+5)^(3/2));

Plot Curvature As A Function Of t

Plot[kap[t],{t,-5,5}, AxesLabel->{"t","Curvature Kappa"}]