Answer
a) $a_T=2.5m/s^2$
b) $a_c=3.08m/s^2$
Work Step by Step
a) The engine causes a net tangential force $\sum F_T=550N$ for a speedboat of mass $m=220kg$. The speedboat's tangential acceleration, therefore, is $$a_T=\frac{\sum F_T}{m}=2.5m/s^2$$
b) We have $a_T=2.5m/s^2, v_0=5m/s$ and $t=2s$. The speedboat's tangential velocity after $2s$ is $$v_T=v_0+a_Tt=10m/s$$
The circular turn's radius $r=32m$, so $$\omega=\frac{v_T}{r}=0.31rad/s$$
The centripetal acceleration can be found by $$a_c=r\omega^2=3.08m/s^2$$
