Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 10

10 The position vector $\vec{r} = 5.00t\hat{i} + (et + ft^2)\hat{j}$ locates a particle as a function of time $t$. Vector $\vec{r}$ is in meters, $t$ is in seconds, and factors $e$ and $f$ are constants. Figure 4-22 gives the angle $\theta$ of the particle’s direction of travel as a function of $t$ ($\theta$ is measured from the positive $x$ direction). What are (a) $e$ and (b) $f$, including units?