The classical mechanics of a particle

A particle in mechanics is like a point in mathematics it has a definite position but no size. This is a useful simplification, when we consider bodies small enough so that their internal structure and motions can be neglected. The most important property of a particle is its mass, m. 

In classical mechanics, every particle follows a definite trajectory, which specifies its position as a function of time. For the moment, we consider a particle moving in one dimension only. We take this as the x direction, so that the trajectory is a function x(t). The velocity of the particle is the differential of position with respect to time, and the acceleration as the differential of the velocity  

The dot notation delned in eqns 2.1 and 2.2 is used to represent differentiation with respect to time. 

Another important quantity is the momentum, p, defined as the product of the mass and the velocity  

The most important equation of mechanics is Newton s Second Law of Motion, This states that the rate of change of momentum is equal to the force acting on the particle. Thus 

---