The location of a moving particle at a particular time is given by \(x=a t-b t^{2}\), where \(a=10 \mathrm{~m} / \mathrm{s}\) and \(b=0.50 \mathrm{~m} / \mathrm{s}^{2}\).

(a) Where is the particle at \(t=0\)?

(b) What is the particle's displacement for the time interval \(t_{1}=2.0 \mathrm{~s}\) and \(t_{2}=4.0 \mathrm{~s}\) ?