1. Suppose the position vector of 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 \(t = 2.00\text{ s}\) to \(t = 4.00\text{ s}\) \([1.00\hat{i} + 0.750\hat{j}\text{ m/s}]\)
b. Determine the velocity and speed at \(t = 2.00\text{ s}\) \([1.00\hat{i} + 0.500\hat{j}\text{ m/s}]\)
