An object moving along the -axis has velocity given by meters per second for
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
An object moving along the x-axis has velocity given by v(t)=(t−2)(t−6) meters per second for 0≤t≤8, where t is measured in seconds.
(a) Determine the exact times in 0≤t≤8 at which the object changes direction. Justify your answer algebraically.
(b) Evaluate the object’s net displacement on the interval 0≤t≤8.
(c) Compute the total distance the object travels during the same interval.
(d) Compare the numerical values obtained in parts (b) and (c), and explain fully why the relationship you observe must hold for any motion with at least one change of direction.