Question

Two objects of the same mass are moving at the same velocity. You give
each the same force, but on one the force is speeding up the object. on
the other it is slowing down the object. Which has a bigger change in
velocity

Answer 1

I would imagine they’d be equal.
F = ma
We can treat mass and force as constants because they do not change throughout both systems and they are the same on both systems. That would mean the acceleration would be the same for both systems.

An explanation of this could be the two forces are acting in different directions, so one is positively accelerating the object and the other is negatively accelerating it