A mouse runs along a baseboard in your house. The mouse's position as a function of time is given by \(x(t)=p t^{2}+q t\), with \(p=0.40 \mathrm{~m} / \mathrm{s}^{2}\) and \(q=-1.20 \mathrm{~m} / \mathrm{s}\). Determine the mouse's average velocity and average speed \((a)\) between \(t=0\) and \(t=1.0 \mathrm{~s}\) and (b) between \(t=1.0 \mathrm{~s}\) and \(t=4.0 \mathrm{~s}\).