For 0≤t≤3 seconds, a particle moving along the x-axis has velocity v(t)=sin(πt)+2, where v is measured in meters per second. At t=0 the particle is 4 meters to the right of the origin.
Respond to each part. Show all steps leading to numeric answers and include units.
(a) Determine the displacement of the particle on the interval 0≤t≤3.
(b) Calculate the particle’s position s(3).
(c) Compute the average velocity of the particle over 0≤t≤3 and interpret this value in terms of the motion.