A car driver going at speed $\mathrm{v}$ suddenly finds a wide wall at a distance $\mathrm{r}$. Should he apply brakes or turn the car in a circle of radius $\mathrm{r}$ to avoid hitting the wall if the retardation to apply brakes is $a_{1 }$and acceleration in circular path is $a_2$

If he applies the breaks, then to stop the car in a distance $\mathrm{r}$

$\therefore a_1=\frac{v^2}{2r}=$ minimum retardation required.

(by friction)

If he takes a turn of radius $\mathrm{r}$, the centripetal acceleration required is

$a_2=\frac{v^2}{r}$ (provided again by friction)

Since $a_1<a_2$, it is better to apply brakes.