A particle moves along a coordinate axis with position given by meters for seconds.
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A particle moves along a coordinate axis with position given by s(t)=t3−6t2+9t+5 meters for 0≤t≤5 seconds.
(a) Determine the particle’s velocity and acceleration as explicit functions of t. Include appropriate units.
(b) For the interval 0<t<5, find all times at which the particle changes direction. Justify your answer.
(c) Identify the time intervals on which the particle is speeding up and on which it is slowing down. Support your intervals with sign charts or equivalent reasoning.
(d) Compute the particle’s total distance traveled on 0≤t≤5 seconds and interpret your result in the context of the motion.