A vibrating string has vertical displacement (in centimeters) modeled by
s(t)=0.8cos(12πt),
where t is time in seconds. Positive displacement indicates upward motion relative to the equilibrium position.
(a) Determine the instantaneous velocity function v(t) of the string.
(b) Calculate the instantaneous velocity at t=0.02 s. State the units of your answer.
(c) Find the smallest positive time t>0 at which the string changes direction from moving upward to moving downward. Justify your answer by analyzing the sign of v(t) immediately before and after this time.