# Fluid mechanics question

Suppose you're driving along a straight, smooth, level stretch of highway with a constant velocity $v$. There is a cup of some fluid in your cup holder. How would you go about finding the angle $\theta$ that the surface of the fluid makes with the bottom of the cup as a function of $v$? And what if you started out with a velocity $v_0$ at time $t=0$ and then accelerated at a constant rate $a$? Can we find $\theta(t)$ without much sweat?

$$\theta = \tan^{-1} \left (\frac{a}{g}\right)$$
where $$a$$ is your acceleration and $$g$$ is gravity.