A particle moving along a coordinate axis has acceleration (in meters per second squared) given by a(t)=sint+2 for 0≤t≤2π. At time t=0 the particle’s velocity is 1 m/s and its position is 3 m.
(a) Find the velocity function v(t) for 0≤t≤2π.
(b) Determine the position function s(t) for 0≤t≤2π.
(c) Compute the particle’s average velocity on the interval [0,2π] and state appropriate units.
(d) Is the average velocity you found in part (c) equal to zero? Justify your answer by referring to the behavior of v(t) over the interval.
(e) Without calculating the total distance traveled exactly, explain whether it must be greater than, equal to, or less than the magnitude of the displacement on [0,2π]. Provide reasoning based on the velocity function.
(a) Find v(t) given a(t) and the initial condition.
(b) Determine s(t) given the initial position.
(c) Compute the average velocity on [0,2π].
(d) Decide whether the average velocity is zero with justification.
(e) Compare total distance traveled with displacement and justify.