A particle moves along a straight line with position given by s(t)=t4−8t2+10 meters for 0≤t≤5 seconds, where t is measured in seconds.
Use calculus to investigate the concavity of the position function and interpret your findings in the context of motion.
(1) Determine expressions for the velocity v(t) and acceleration a(t) of the particle.
(2) Find the open time intervals on 0<t<5 during which the graph of s is concave up and those during which it is concave down.
(3) Identify every time t in 0<t<5 at which the graph of s has a point of inflection. Give the coordinates (t,s(t)) of each such point.
(4) Explain what an inflection point on the graph of s signifies about the particle’s change in motion. Relate your explanation to the sign of the acceleration.