In a physics experiment, the vertical displacement s(t) (in meters) of a vibrating string at time t seconds is modeled by
s(t)=100sec(0.2t)
for all t in the domain of the function.
(a) Determine the instantaneous velocity s′(t) of the string as a function of t. Express your answer in meters per second.
(b) Compute the instantaneous velocity at t=π seconds. Give both the exact value and the appropriate units.
(c) Interpret the sign of the velocity obtained in part (b) in terms of the motion of the string at t=π seconds.