Parametric Curve Acceleration

Calculus

$\large{x = \sin(t) \quad \quad y = \sin^{2}(t)}$

A particle in the $xy$ plane has coordinates that vary with time as shown above. $|a|$ denotes the magnitude of the particle's acceleration. Consider the following ratio:

$\frac{| a |_{x = 0}}{| a |_{x = 1}} = \frac{A}{\sqrt{B}}$

If $A$ and $B$ are coprime positive integers, determine $A+B$ .