Consider the following two situations:

A) A person pushes on a wall without moving.

B) A person runs and accelerates.

For each case, answer the following questions:  

- Identify the relevant forces acting on the person

- Does Newton’s Third Law apply? If it applies, what are the 3rd law pairs?  

- Why is/isn't the person accelerating?

A) Anytime an object applies a force to another object, there is an equal and opposite force back on the original object.

If you push on a wall you feel a force against your hand the wall is pushing back on you with as much force as you apply to it.

yes the third law applies, the normal force and person applying force make a action reaction pair.

the person isnt accelearting because the forces are balanced.

B) the forces are normal force due to ground,

man putting force on ground that has bot horizontal and vertical comonents.

yes , third law appies here too , the the ground normal force, and component of persons vertical force form a action reaction pair.

the person does accelerates , but in horizontal direction,As the man runs, his feet are exerting a force on the ground, and the ground is exerting the same force, equal but opposite(direction), to his feet. Newton's third law does apply here. Newton's 2nd law of acceleration applies here too. As the man increases his force applied on the ground while running horizontally, he is more likely to accelerate.