Velocity from external objects

I'm making a platformer and I'm moving the player at constant speed while running. This is the initial code that was used for movement:

 myRigidbody.velocity = new Vector2 (Input.GetAxis("Horizontal") * movementSpeed, myRigidbody.velocity.y);

The problem is that the player won't receive additional velocity from external objects. A couple examples:

• Standing on a moving platform. The player won't move along with it.

• Standing on a conveyor (Surface Effector 2D). The player won't move along with it.

I've figured out that the player wasn't moving along with those objects because it's X velocity was ALWAYS being set to 0 while not pressing the movement key so I fixed this by only setting the X velocity to 0 ONCE at the moment when the player stops running. The remaining problem:

• While running on a moving platform or a conveyor (Surface Effector 2D) the additional velocity from these objects are not taken into account. For example - if the player has a movement speed of 10 and the conveyor is moving at a movement speed of 2 then when the player is running on the conveyor his total speed should be 10+2, but instead it's just 10.

I've had to find a way so that the player would run at a constant speed, while still being affected by external velocities. So this was my try at that:

 // "currentWalkSpeed" keeps track of what speed the player is running at currently
 
                     // True only ONCE, when the player stops moving or changes running direction
                     if (prevHorizontal != horizontal && prevHorizontal != 0) {
                         // Stop the player
                         myRigidbody.velocity = new Vector2 (0, myRigidbody.velocity.y);
                         // Reset the walking/running speed buffer
                         currentWalkSpeed = 0;
                     }
                       
                     // Calculate how much velocity we lost due to friction so we know how much to add to keep running speed constant
                     if (horizontal * prevVelocity > horizontal * myRigidbody.velocity.x) {
                         // Calculate how much velocity we lost due to friction
                         float velocityDiff = prevVelocity - myRigidbody.velocity.x;
                         // Current walking/running speed goes down due to friction
                         currentWalkSpeed -= velocityDiff;
                     }
 
                     prevHorizontal = horizontal;
 
                     // True if the player is not yet running at the constant speed. For example if it lost some speed due to friction
                     if (Mathf.Abs(currentWalkSpeed) < movementSpeed) {
                         // Calculate how much force we have to add to keep the player moving at constant speed
                         float diff = movementSpeed - Mathf.Abs (currentWalkSpeed);
 
                         // Add the force
                         myRigidbody.AddForce (Vector2.right * horizontal * diff, ForceMode2D.Impulse);
                         // Update the current walking/running speed
                         currentWalkSpeed += (horizontal * diff);
                     }
 
                     prevVelocity = myRigidbody.velocity.x;

This solution worked well, but there's a bug I can't solve:

• If the player is running at a movement speed of 10 and while still running he lands on a conveyor that is moving of movement speed of 2, the player is still moving of a movement speed of 10 instead of 10+12. Only when I release the movement key and stop the player on a conveyor and press the movement key again, only then the player is running at a speed of 10+2 how he should.

Thank you very much for reading if you've got this far. I've been stuck on this problem for a week now and I'm contemplating whether I should drop the physics and just write up an additional script to objects with velocity which would transfer their velocity on collision with other objects where I could simply add that additional velocity to the current velocity of the object if needed. Any pros and cons to these two solutions?