Newton's Law says that for every action force there is a reaction force of the same magnitude in the opposite direction. If this is true, how can a child pull a wagon? Won't the wagon pull back just as hard?

This is a question I sometimes use to challenge my students' thinking. I phrase it as "how can a car pull a trailer (or a horse pull a cart) when the forward force of the car on the trailer is equal to the backward force of the trailer on the car?"

I prefer not to talk about 'action' and 'reaction' forces: there is nothing specific that makes a force one or the other, it just depends what we are paying attention to. My preferred way of stating Newton's Third Law is as follows:

For every force, there is another force of equal magnitude, acting in the opposite direction. These forces act on different objects.

In this case, the child exerts a force in one direction on the wagon, and Newton's Third Law says that the wagon exerts a force of the same magnitude (size) on the child in the opposite direction. If the child increases her force, the wagon increases its force. The Law says the forces are always exactly equal.

So how can the child move the wagon?

The key to this question is that it directs our attention to the wrong pair of forces. There is also a downward force of the child on the earth, and an upward force of the earth on the child. Similarly for the wagon. And so on. There are many force pairs acting.

The one that allows the linked system of child+wagon to move is that the child exerts a force 'backward' on the earth, and the earth exerts a force 'forward' on the child's feet on the earth. Now, these forces are equal in magnitude, but now we need to invoke Newton's Second Law :

When a force is exerted on an object, the acceleration of the object is directly proportional to the magnitude of the force and inversely proportional to the object's mass.

The forces on the earth and the child are the same, but the child's mass may be #30 kg# and the earth's mass is about #6 * 10^24 kg#.

The child and the wagon will accelerate forward quite a lot, and the earth will accelerate backward so little we can't notice it. But this is the 'action and reaction' force pair we need to consider to explain why the wagon can accelerate.