**Principles in the formation of the Equation of Motion of a Particle :-**

**For Motion in Straight Line ;**Let the mass of the body (particle) be

**m**and let the distance of the particle measured from a suitable origin be

**x**at the time

**t**.

Then acceleration is

**(d/dt)(dx/dt)**

therefore by Second Law of Motion

**m[(d/dt)(dx/dt)]**= Forces in the direction of

**x**increasing

The forces usually are ;-

1)---

**g**vertically downwards in a gravitational field like earth .

2)--- tension in a string

3)--- reactions or stress at point where the point may be in contact with other particles .

4)--- forces of attraction

5)--- forces of resistance to motion by any means may be by atmosphere , friction, winds or by any other means .

In taking the forces we must fix the sign properly if the forces acts along the line .

If a force

**F**acts at an angle

**A**to the straight line , then the resolved part of the force along the line is

**FcosA**. If

**g**acts on on a particle and if the particle is moving along the horizontal line , then

**g**, being vertical , has no resolved part horizontally and

**g**does not effects the Motion .

Also note that velocity,

**v=dx/dt**, and acceleration

**(d/dt)(dx/dt) = dv/dt = (dx/dt)(dv/dx) = v(dv/dx)**

**For Motions in two dimension;**Let two perpendicular axes are

**X**and

**Y**at the plane of motion . The forces are resolved in these two directions and respectively

**m(d/dt)(dx/dt)**

**and m(d/dt)(dy/dt)**