# How to calculate new velocities between resting objects (AABB) after accelerations?

lately I have been trying to create a 2D platformer engine in C++ with Direct2D. The problem I am currently having is getting objects that are resting against each other to interact correctly after accelerations like gravity have been applied to them.

Right now I can detect collisions and respond to them correctly (I think) and when objects collide they remember what other objects they're resting against so objects can be pushed by other objects (note that there is no bounce in any collisions so when objects collide they are guaranteed to become resting until something else happens). Every time the simulation advances, the acceleration for objects is applied to their velocities (for example vx += ax * t, where t is time elapsed since last advancement).

After these accelerations are applied, I want to check if any objects that are resting against each other are moving at different speeds than their counterparts (as different objects can have different accelerations) and depending on that difference either unlink the two objects so they are no longer resting, or even out their velocities so they are moving at the same speed once again. I am having trouble creating an algorithm that can do this across many resting objects.

Here's a diagram to help explain my problem