Starting from rest heavier objects require more force to cover the same distance as lighter objects, in the same time. Which law can explain this scenario?
Second law of motion
Given, both heavier and lighter objects take the same time to cover the same distance. I.e. the velocity of the objects at the destination is the same.
The question is about the impact or momentum change. The impact of an object depends on mass and velocity. Since in this case, the heavier object has more mass, the change in momentum in high. So, a larger force is required by heavier objects.
The law that relates the change in momentum to force is the Second Law of Motion.