Answer
The minimum possible time for this U-turn is 4.06 seconds.
Work Step by Step
We can find an expression for the speed:
$a_r = \frac{v^2}{r}$
$v = \sqrt{a_r~r}$
We can find an expression for the time:
$T = \frac{d}{v}$
$T = \frac{\frac{1}{2}(2\pi~r)}{\sqrt{a_r~r}}$
$T = \frac{\pi r}{\sqrt{a_r~r}}$
$T = \pi~\sqrt{\frac{r}{a_r}}$
To minimize the time, we should minimize the radius $r$.
The minimum radius is $5.0~m$. We can find the time $T$:
$T = \pi~\sqrt{\frac{r}{a_r}}$
$T = \pi~\sqrt{\frac{5.0~m}{3.0~m/s^2}}$
$T = 4.06~s$
The minimum possible time for this U-turn is 4.06 seconds.
