b
\({a_c} = {k^2}r\,{t^2}\)

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

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

\(\therefore v = k\,r\,t\)

\({a_t} = \frac{{dv}}{{dt}} = k\,r\)

\(P = {F_t}v \,= m\,{a_t}v \,=m(kr) \,krt \,= m{k^2}{r^2}t\)