Consider the position function \(x(t)=p+q t+r t^{2}\) for a moving object, with \(p=+3.0 \mathrm{~m}, q=+2.0 \mathrm{~m} / \mathrm{s}\), and \(r=-5.0 \mathrm{~m} / \mathrm{s}^{2}\).

(a) What is the value of \(x(t)\) at \(t=0\) ?

(b) At what value of \(t\) does \(x(t)\) have its maximum value?

(c) What is the value of \(x(t)\) at this instant?

(d) Draw a position-versus-time graph.

(e) Describe the behavior of an object that is represented by this function. \((f)\) How far has the object traveled in these intervals: From \(t=0\) to \(t=0.50 \mathrm{~s}\) ? From \(t=0\) to \(t=1.0 \mathrm{~s}\) ? From \(t=0.50 \mathrm{~s}\) to \(t=1.0 \mathrm{~s}\) ?