MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
For a particle moving along a straight line, the position at time t seconds is given by x=4t2−16t+5 metres for 0≤t≤6.
(i) Calculate the displacement of the particle between t=1s and t=5s.
(ii) Determine the average velocity during this interval, stating its magnitude, sign and unit.
(iii) Without differentiating, explain from the form of x(t) whether the average velocity you obtained is the maximum, minimum, or neither among all possible 4-s intervals inside 0–6s. Justify briefly.