A particle moves along the x-axis with position described for 0≤t≤6 seconds by
s(t)=41e0.8t−21sin(πt),
where s is measured in meters.
(a) Obtain a simplified expression for the particle’s velocity v(t).
(b) Show algebraically that v(t)=0.2e0.8t−2πcos(πt).
(c) Determine, to three decimal places, the time(s) in 0≤t≤6 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.