Askateboarder pushes the skateboard into motion by applying a backward force on the road. which of newtons laws of motion is most relevant to this activity?

the third law (for every action there is an equal and opposite reaction).

Newton's first and third law.

From the scene described above, the skateboard was initially at rest and by Newton's first the skateboard would continue to remain in its state of rest. This law which states that a body will continue to be at rest or continue in a state of uniform motion with constant velocity unless acted upon by an external or net force (in a situation where not only one force is in action). From this law the skateboard would need an external supply of force for it to be put into motion which the skateboarder supplies indirectly.

The skateboarder pushes backwards on the road (that is he applies a force on the road in a direction opposite the direction of intended motion). By Newton's third law, this action of the skateboarder causes an equal reaction of the road on the skateboarder in the opposite direction. Newton's third law states that action and reaction are equal but opposite in direction. So, the road in response to this backward force pushes the skateboarder in the forward direction causing the skateboarder and the skateboard to move in the forward direction.

Thank you for reading.

we need to know the time interval during which the force acts. impulse of force = momentum change