# Newton's second law

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**Newton's second law** of motion, one of the most important in physics, states that the force which, acting on a body, is necessary to produce a change in its motion is proportional to its mass and to the acceleration (the time derivative of its velocity). Thus it can be written as **F** = *km***a** (where **F** and **a** are understood as vector quantities). It may also be stated as **F** = *k*(^{dp}/_{dt}, where **p** represents the momentum vector.

If the units of force, mass, and acceleration (or of force, momentum, and time) are chosen appropriately, the constant *k* in the above equations may be taken to be 1. Many physicists consider that any system of units in which the constant *k* has to be taken different from 1 is "incoherent," and refuse to recognize that physical calculations can be made in such systems without any problem, simply choosing the correct value of *k.* However, this is equivalent to assuming that Newton's second law has a significance greater than all other laws of motion which contain a constant in their formulation. It is perfectly consistent with the laws of physics to give a constant appearing in some other equation a unit value, It is even possible to set *k* to any value one chooses, without requiring any other constant in a law of physics to be 1, if that is useful, and such a formulation will still be consistent with the laws of physics.