Newton's first law says that an object in motion will remain in motion in the same direction unless acted upon by an outside force; an object at rest will remain at rest unless acted upon by an outside force.

In the example of the car hitting the wall, the passenger continues travelling at the same speed that the car was moving directly before impact. He does not stop his forward motion until an outside force (his seatbelt) stops him.

In the example of the satellite, the rotation of the satellite can only change rate if an outside force interferes. Because there are no forces to affect the satellite's spinning, it will continue to do so as per Newton's first law.

In the example of the construction worker, the box was at rest and therefore resisted any change to being at rest. Once it is in motion, it will continue in motion in the same direction. This principle is the same reason why static coefficients of friction are generally greater than kinetic coefficients of friction.

In the example of the child on the merry-go-round, the important part of Newton's first law to recall is that objects will remain in motion in the same direction. The rotational motion of the child will result in a constantly changing velocity in the direction tangent to the edge of the ride. Once the child lets go, she will move in a straight line directly off of the ride.

The hammer and nail example illustrates Newton's third law, but has no bearing on the principle of inertia.

This is an example of Newton's first law: an object at rest will remain at rest, and an object in motion will remain in motion in that direction, unless acted upon by an outside force.

Inertia is effectively nature's way of trying to avoid change. This explains why the box is hard to move while it is still; it requires change to get it to move from rest to moving. It is easier to continue motion when it is moving because it requires much less change to keep it moving in the same direction.

Mathematically, this principle dictates that the coefficient of static friction will always be greater than the coefficient of kinetic friction.

While the bus in moving forward, you move forward with the bus at the same velocity.

When the bus stops, your body continue to move forward with the original velocity at which you had been traveling. Since you are not attached to the bus, you will not stop at the same rate as the bus and will fall forward as your body continues to move.

This is the reason why seatbelts are so important as it keeps you fixed to the car so that you undergo the same forces that are acting on the car.

While the truck in moving forward, the carte moves forward with the truck at the same velocity.

When the trucks stops, the crate continues to move forward with the original velocity at which it had been traveling since there is no friction to stop the crate from moving. Since the crate is not attached to the truck, it will not stop at the same rate as the truck and will slide toward the cab of the truck as the truck slows down.

This is the reason why tie-downs are so important as it keeps objects fixed to the truck so that they undergo the same forces that are acting on the truck.

Newton's first law says that an object in motion will remain in motion in the same direction unless acted upon by an outside force; an object at rest will remain at rest unless acted upon by an outside force.

In the example of the car hitting the wall, the passenger continues travelling at the same speed that the car was moving directly before impact. He does not stop his forward motion until an outside force (his seatbelt) stops him.

In the example of the satellite, the rotation of the satellite can only change rate if an outside force interferes. Because there are no forces to affect the satellite's spinning, it will continue to do so as per Newton's first law.

In the example of the construction worker, the box was at rest and therefore resisted any change to being at rest. Once it is in motion, it will continue in motion in the same direction. This principle is the same reason why static coefficients of friction are generally greater than kinetic coefficients of friction.

In the example of the child on the merry-go-round, the important part of Newton's first law to recall is that objects will remain in motion in the same direction. The rotational motion of the child will result in a constantly changing velocity in the direction tangent to the edge of the ride. Once the child lets go, she will move in a straight line directly off of the ride.

The hammer and nail example illustrates Newton's third law, but has no bearing on the principle of inertia.

This is an example of Newton's first law: an object at rest will remain at rest, and an object in motion will remain in motion in that direction, unless acted upon by an outside force.

Inertia is effectively nature's way of trying to avoid change. This explains why the box is hard to move while it is still; it requires change to get it to move from rest to moving. It is easier to continue motion when it is moving because it requires much less change to keep it moving in the same direction.

Mathematically, this principle dictates that the coefficient of static friction will always be greater than the coefficient of kinetic friction.

According to Newton’s First law, an object in motion will remain in motion until there is an external force acting on this.  This is observable in the real world as marbles will continue to roll until they are slowed down by friction or stopped by a wall or a person or some other external force.