A particle moves on a predetermined trajectory with the equation of motion (s(t)=k t^{2}), with (k) constant

Question:

A particle moves on a predetermined trajectory with the equation of motion $s(t)=k t^{2}$, with $k$ constant and with magnitude of the acceleration equal to $a=2 k$. Show by using (3.74) that the radius of curvature is given by the relation $ho=\frac{v^{2}}{\sqrt{a^{2}-\stackrel{s}{s}^{2}}}$. Show that in the present case the motion is rectilinear.

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