d. Now you pull your sister across the floor so that she moves with increasing speed (accelerates). Compare the magnitude of the force exerted by you on your sister, with the magnitude of the force she exerts on you. Are they the same or different? If they are not the same, which is larger? Why or why not?

are they the same (newtons third law)

or do you exert a force on your sister (since she accelerates)?

Newton's third law applies, regardless of who accelerates more. Perhaps one of you accelerates more than the other, or is restrained by other forces. It doesn't matter. Bodies apply equal and opposite forces upon one another.

According to Newton's third law of motion, "For every action, there is an equal and opposite reaction." This means that if you exert a force on your sister, she will exert an equal and opposite force on you. So, in this situation, the magnitudes of the forces exerted by you on your sister and by your sister on you would be the same.

Now, let's focus on the scenario where you're pulling your sister across the floor and she moves with increasing speed (accelerates). In order for your sister to accelerate, there must be a net force acting on her. This force can be generated by you pulling her with a certain amount of force.

Since you are the one pulling your sister, you are exerting a force on her. According to Newton's third law, your sister will exert an equal and opposite force on you. Therefore, the magnitude of the force exerted by you on your sister and the magnitude of the force she exerts on you would be the same.

In summary, the forces exerted by you on your sister and by your sister on you are the same (as per Newton's third law), even though your sister is the one experiencing the acceleration.