1. Suppose the position vector for a particle is given as a function of time by \(\vec{r}(t) = x(t)\hat{i} + y(t)\hat{j}\), with \(x(t) = at + b\) and \(y(t) = ct^2 + d\), where \(a = 1.00\text{ m/s}\), \(b = 1.00\text{ m}\), \(c = 0.125\text{ m/s}^2\), and \(d = 1.00\text{ m}\). (a) Calculate the average velocity during the time interval from \(t = 2.00\text{ s}\) to \(t = 4.00\text{ s}\). (b) Determine the velocity and the speed at \(t = 2.00\text{ s}\).
