Figure shows the velocity and acceleration of a point like body at the initial moment of its motion. The acceleration vector of the body remains constant. The minimum radius of curvature of trajectory of the body is 

The acceleration vector shall change the component of velocity ${\mathrm{u}}_{\parallel }$ along the acceleration vector. 

$\mathrm{r}=\frac{{\mathrm{v}}^2}{{\mathrm{a}}_{\mathrm{n}}}$

Radius of curvature r_min means v is minimum and a_n is maximum. This is at point P when the component of velocity parallel to acceleration vector becomes zero, that is ${\mathrm{u}}_{\parallel }=0.$