Perhaps you're right, but I saw it as integration. The ball is falling to earth at Vf=Vo+1/2at^2, the dog integrates to get the velocity Vf and thus position t

Perhaps you're right, but I saw it as integration. The ball is falling to earth at Vf=Vo+1/2at^2, the dog integrates to get the velocity Vf and thus position to find the point in space to run/jump and time his catch in mid-air.