I was riding a bus one day and noticed that the double windows had some water between them. As the bus accelerated, the water collected to the sides, first forming a trapezoid and then a right triangle.
I begun wondering how it would be possible to measure the acceleration using only the geometry of the form of the amount of water.
Like, assume that at $a=0$ the water has height $h$ and width $w$. As the bus accelerates, at some time $t_1$ the water forms a trapezoid with the shorter side $h_1$ ans longer side $h_2$. The bottom has same width $w$.
At time $t_2$ water has formed a triangle with height $H$ and width $w$ (the last moment it touches the other side of the glass). And finally at time $t_3$ the height is $y$ and the width is $W$.
In each situation, what is the acceleration of the bus?