Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 11

11 A particle that is moving in an xy plane has a position vector given by $\vec{r} = (3.00t^3 - 6.00t)\hat{i} + (7.00 - 8.00t^4)\hat{j}$, where $\vec{r}$ is measured in meters and $t$ is measured in seconds. For $t = 3.00 \text{ s}$, in unit vector notation, find (a) $\vec{r}$, (b) $\vec{v}$, and (c) $\vec{a}$. (d) Find the angle between the positive direction of the x axis and a line that is tangent to the path of the particle at $t = 3.00 \text{ s}$.