The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt 1 3 cos πt, where t is measured in seconds.

(a) Find the average velocity during each time period:

(i) [1, 2] 

(ii) [1, 1.1]

(iii) [1, 1.01] 

(iv) [1, 1.001]

(b) Estimate the instantaneous velocity of the particle when t − 1.