A particle moves along the -axis with position described for seconds by s(t)= 14e^…

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

Problem

A particle moves along the xx-axis with position described for 0≤t≤60\le t\le6 seconds by s(t)=14e0.8t−12sin⁡(πt),s(t)=\tfrac14e^{0.8t}-\tfrac12\sin(\pi t), where ss is measured in meters. (a) Obtain a simplified expression for the particle’s velocity v(t)v(t). (b) Show algebraically that v(t)=0.2e0.8t−π2cos⁡(πt)v(t)=0.2e^{0.8t}-\dfrac{\pi}{2}\cos(\pi t). (c) Determine, to three decimal places, the time(s) in 0≤t≤60\le t\le6 at which the velocity attains an absolute maximum and an absolute minimum. Justify each answer using appropriate calculus arguments. (d) For each extreme velocity value found in part (c), interpret its physical significance in the context of the particle’s motion.

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