A particle moves along a straight track with acceleration a(t)=12t-30 meters per…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A particle moves along a straight track with acceleration
a(t)=12t−30meters per second squared
for 0≤t≤5 seconds. At t=0 the particle’s velocity is 24 m/s and its position is 10 m to the right of the origin.
(a) Determine the particle’s velocity function v(t) for 0≤t≤5.
(b) Find the position function s(t) for 0≤t≤5.
(c) Compute all critical times in 0≤t≤5 for the position function and classify each as a local maximum, local minimum, or neither. Include justification.
(d) Identify the particle’s greatest distance from the origin during 0≤t≤5 and state the time at which it occurs, supporting your conclusion with calculus-based reasoning that addresses endpoints as well as critical points.
(e) For the time found in part (d), determine the sign of the acceleration and interpret its physical implication for the particle’s subsequent motion.