Parametric Curve Acceleration

Calculus Level 4

x=sin(t)y=sin2(t)\large{x = \sin(t) \quad \quad y = \sin^{2}(t)}

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

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

If AA and BB are coprime positive integers, determine A+BA+B.


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