An object moves along a straight path with acceleration meters per second squared for
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
An object moves along a straight path with acceleration a(t)=cost−1.2 meters per second squared for 0≤t≤2π. At time t=0 the object’s velocity is 5 meters per second and its position is 0 meters.
(a) Derive an explicit expression for the velocity v(t) on 0≤t≤2π.
(b) Determine all time intervals within 0≤t≤2π during which the object moves in the negative direction.
(c) Compute the object’s net displacement on 0≤t≤2π.
(d) Compute the total distance traveled by the object on 0≤t≤2π.