b
\(s = \frac{{{t^2}}}{2} + \frac{{{t^3}}}{3}\)

\( \Rightarrow v = \frac{{ds}}{{dt}} = t + {t^2}\)

\({a_t} = \frac{{dv}}{{dt}} = \frac{d}{{dt}}(t + {t^2})\) \( = 1 + 2t\)

\(t = 2 \,sec, \,v = 6 \,m/s, \, {a_t} = 5\,m/{s^2}\)

\({a_c} = \frac{{{v^2}}}{r} = \frac{{36}}{3} = 12\,m/{s^2}\)

\({a_N} = \sqrt {a_c^2 + a_t^2} \, = \sqrt {{{(12)}^2} + {{(5)}^2}} \, = 13\,m/{s^2}\).