# Parametric Curve Acceleration

Calculus Level 4

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

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 $$A+B$$.

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