An object moves along a straight path with acceleration meters per second squared for
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
An object moves along a straight path with acceleration a(t)=2t−6 meters per second squared for 0≤t≤5. At time t=0, its velocity is v(0)=4 meters per second in the positive direction.
(a) Find the object’s velocity function v(t) for 0≤t≤5.
(b) Determine all times t in the interval 0≤t≤5 when the object is at rest. Justify your answer.
(c) Calculate the total distance, in meters, traveled by the object on the interval 0≤t≤5. Organize your work to make clear how you handle intervals of forward and backward motion.
(d) Suppose instead that the object experienced the same acceleration for 0≤t≤5 but started with velocity v(0)=−4 meters per second. Without recomputing integrals, predict and justify how the total distance traveled would compare to that found in part (c).