Velocity and Acceleration

 

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 )