Given that \({a_C} = {k^2}r{t^2}\) and \({a_C} = \frac{{{v^2}}}{r}\)

\(\frac{{{v^2}}}{r} = {k^2}r{t^2}\)

or \({v^2} = {k^2}{r^2}{t^2}\) or \(v = krt\)

Tangential acceleration \(a = \frac{{dv}}{{dt}} = kr\)

Now force \(F = m \times a = mkr\)

So power \(P = F \times v = mkr \times krt = m{k^2}{r^2}t\)