To answer this question we should know following key points:

1. Total Acceleration is given as $a_{total}=\sqrt{\left(a_t\right)^2+\left(a_n\right)^2}$

2. $a_t=\dfrac{dv}{dt} \text{ and } a_n=\dfrac{v^2}{\rho}$

Here, $s=0.5t^3+3t \text{ m }$

$\therefore v=\dfrac{ds}{dt}=1.5t^2+3 \text{ m/s}$

and 

$a_t=\dfrac{dv}{dt}=3t \text{ m/$s^2$}$ Hence, at t = 2 sec, $v=1.52^2+2=9 \text{ m/s }$and$a_t=32=6 …