A particle begins moving at time t=0 seconds with velocity v(0)=3 m/s. Its acceleration for 0≤t≤2π seconds is given by a(t)=sint meters per second squared.
(a) Derive an explicit expression for the velocity v(t) for 0≤t≤2π.
(b) Find all times in 0≤t≤2π at which the particle changes direction. Justify your answer.
(c) Compute the total distance traveled by the particle during the time interval 0≤t≤2π. Include units in your answer.