**Velocity and Acceleration of a Moving Particles :-**

If a particle is moving along a straight line , and if at any instant

**t**the position

**P**of the particle be given by the distance

**s**measured along the path from a suitable fixed point

**A**on it , then

**v**denoting the velocity and

**f**the acceleration of the particle at the instant ,

We have;

**v = rate of displacement**

**= rate of change of s with respect to time**

**= ds/dt ;**

**and , f = rate of change of velocity with respect to time**

**= dv/dt**

**= ( d/dt ) ( ds/dt )**

If instead of moving in a straight line , the particle be moving in any manner in a plane , the position of a particle at any instant

**t**being given by the Cartesian Co-ordinates

**x , y**referred to a fixed set of axes the components of velocity and acceleration parallel to those axes will similarly be given by

**vx = rate of displacement parallel to x-axis = dx/dt**

**vy = rate of displacement parallel to y-axis = dy/dt**

**fx = rate of chang of vx = ( d/dt ) ( dx/dt )**

**fy = rate of change of vy = ( d/dt ) ( dy/dt )**