A particle moves along the lemniscate defined by

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A particle moves along the lemniscate defined by (x2+y2)2=5 (x2−y2)(x^{2}+y^{2})^{2}=5\,(x^{2}-y^{2}), where coordinates are in meters and time in seconds. At a certain instant the particle is in the first quadrant at the point for which x=1x=1 and y>0y>0. At this moment dxdt=0.60 m s−1\dfrac{dx}{dt}=0.60\text{ m s}^{-1}. (a) Determine the corresponding yy-coordinate of the particle. (b) Calculate dydt\dfrac{dy}{dt} at this instant. (c) Find the particle’s instantaneous speed and state whether the particle is moving toward or away from the origin. Justify your answer.

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