In my previous post on solving projectile motion problems graphically, I mentioned that it should be possible to overlay the trajectory of the projectile onto this construction and animate it in geogebra. After some fiddling with geogebra, I was able to produce this video.

In the animation, $\Delta v$ increases with time, and the average velocity is computed as the sum of $v_i$ and $\frac{\Delta v}{2}$. When this vector is scaled by the time ($\vec{\Delta r}=\vec{v}_{avg}t$), you get a displacement vector from the origin to the current location of the projectile.

If you want to play with the improved geogebra file, here’s a link.