Newton's laws are fundamental laws of classical mechanics. Any task comprising though some share of mechanics of the movement of a body or a material point does not do without application of these rules.
The first law of Newton
The first law of Newton enjoys quite low popularity in connection with small practical applicability. Actually, use of this law meets very often, just it is accepted by default. The wording of this rule says that the uniform rectilinear motion is absolutely equivalent to a condition of rest of a body. It seems that this regularity has no practical importance, but it not so. There is a lot of tasks applying the first law Newton. For example, present that in a task speeds of the movement of two bodies concerning the earth are given, and it is necessary to find the size of one of speeds concerning other body. It is a typical problem of school physics of middle school. Application of the first law in this task comes down to a possibility of transition to the system of coordinates connected with the second body. In the system of coordinates of this body its speed is considered zero due to application of the first law of Newton.
The second law of Newton
The second law of Newton expresses communication between the acceleration acquired by a body, its weight and force causing this acceleration. Other formulation says that the relation of change of an impulse by the time of change gives value of force. Application of a formula of the second law of Newton is useful almost in each classical task in physics. In some tasks you are given distribution of forces operating on a body and its weight with need to find expression for body speed. For its decision all available forces are inserted into total amount in the ratio of the second law of Newton and are divided into body weight. Thus, you receive expression for acceleration of a body. And acceleration, as we know, is derivative of function of speed of a body. Means, having integrated expression for acceleration, it is possible to find speed.
Various versions of wording of the second law of Newton are possible. Therefore its look depends on this specific objective. In the school textbook in physics the ratio of the work of weight on acceleration is given. However if, say, to consider the above-stated task, then it will be correct to write down a formula of the second law of Newton, having replaced the size of acceleration derivative of speed. If it is necessary to find a trajectory or the equation of the movement of a body in the same task, then the size of acceleration should be written down as the second derivative of body coordinate, and further to integrate it twice.
The third law of Newton
The third law of Newton is applied only in any narrow part of some tasks of the section of mechanics. It says about equality of forces of action and counteraction, that is forces applied to the same body. Effect of this rule comes down to a possibility of mutual compensation of forces operating on the same body which is at rest.