The position of a yo-yo as a function of time is given by \(x(t)=A \cos (p t+q)\), where \(A=0.60 \mathrm{~m}, p=\frac{1}{2} \pi \mathrm{s}^{-1}\), and \(q=\frac{1}{2} \pi\).

(a) Plot this function at 17 equally spaced instants from \(t=0\) to \(t=8.0 \mathrm{~s}\).

(b) At what instants is the velocity zero?

(c) Plot the \(x\) component of the velocity as a function of time over the time interval from \(t=0\) to \(t=8 \mathrm{~s}\).