Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 6

An electron’s position is given by \(\vec{r} = 3.00t \hat{i} - 4.00t^2 \hat{j} + 2.00 \hat{k}\), with \(t\) in seconds and \(\vec{r}\) in meters. (a) In unit-vector notation, what is the electron’s velocity \(\vec{v}(t)\)? At \(t = 2.00 \text{ s}\), what is \(\vec{v}\) (b) in unit-vector notation and as (c) a magnitude and (d) an angle relative to the positive direction of the \(x\) axis?