If all forces acting on an object are balanced (i.e their sum is equal to zero), then the object will either be at rest or moving with constant velocity.
Another way of stating the law:
If the sum of all forces acting on an object is equal to zero, then the acceleration of that object is equal to 0 and therefore its velocity does not change. If it is rest it says at rest and if it is moving a constant velocity it stays at that same velocity.

Example 1

What force is needed so that a 100 Kg box moving on a frictionless floor on a straight line at the speed of 1 m/s keeps moving for another 100 minutes in the same direction at the same speed?
Solution
The forces acting on a box on the floor are balanced: The weight is balanced by the normal force that the floor exerts on the box. Since there is no friction, then according the Newton's first law no force in needed and the box keeps moving at the same velocity as long as no net force acting on the box is balanced.

Newton's Second Law

The net force F acting on a body is equal to its inertial mass m multiplied by its acceleration a.

∑ F = m a (Note: F and a are vector quantities)

Another way of stating the law:
If the sum of all forces acting on an object is not equal to zero, then that object will accelerate according to the law ∑ F = m a. Since mass m is a scalar, the object will accelerate in the direction of the net force ∑ F.

Example 2

One force of 30 N acting East and a second second force of 30 West on an object of a mass m = 20 Kg. What is the magnitude and direction of the acceleration a of the object?
Solution
The two forces have equal magnitude but opposite direction (East and West) and therefore their sum is equal to 0. Hence according to the Newton's second law, we have
0 = m a
Since m is not equal to 0 then the acceleration a = 0.

Example 3

One force of 30 N acting East and a second second force of 20 West on an object of a mass m = 20 Kg. What is the magnitude and direction of the acceleration a of the object?
Solution
The two forces acts in different directions, hence the magnitude of the sum of the forces is
30 - 20 = 10 N
The direction of the sum is East because this is the direction of the force with the larger magnitude. Hence using the second law on Newton
10 = m a
a = 10 / 20 = 0.5 m/s^{2}
The object accelerates to the East at 0.5 m/s^{2}.

Newton's Third Law

For every action, there is an equal (in magnitude) and opposite reaction.
Two important things about the action and reaction forces
1) Action and reaction forces exist in pairs,
2) Each of the action and reaction forces act on a different object.

Example 4

When a person pushes a trolley with a force F1, the trolley also exerts a force F2 on the person. F1 acts on the trolley and F2 acts on the person. F1 and F2 acts on two different objects.
NOTE IN ORDER to AVOID CONFUSION: Since the forces are equal in magnitude and opposite in direction, their sum is equal to 0; why is there an acceleration of the trolley? Because the two forces are acting on different objects. Newton's second law is about the net force on a single object. So in order to understand why the trolley is accelerates when pushed, we need to consider all forces acting on the trolley ONLY.

Example 5

The tires pushes on the road and the road pushes on the tires and hence the car moves.

Example 6

Where is the reaction to the weight of a falling object?
Earth exerts a force on the falling object but the object also exerts a force on the earth and because of its large mass, the acceleration of the earth is much smaller than that of the object.

Some Important Applications of The Third Law of Newton

Example 7

The engine to send a rocket into space works according to the third law of Newton.
The combustion of the fuel inside the rocket results in gases escaping at very high speed in a given direction and the rocket moving into the opposite direction.

Example 8

Air escaping from a balloon, pushes the balloon in the opposite direction.

Example 9

Jet engines also works on the principle of the third law of Newton: high speed gases are ejected from the back of the jet engine producing a movement of the jet in the opposite direction.

Example 10

The rotating tires of a moving bicycle pushes the road backward and the road reacts by pushing the bicycle forward. These are forces of friction between the tires and the road.