Motion of a Particle in Space

 1 In a Nut Shell:  A particle can be located by its position vector,  r,  in space.  Description of its motion involves both its velocity vector, v,  and its acceleration vector,  a .   Let    r  =  (x, y, z)  be a position vector from the origin, O,  to an arbitrary point P(x,y,z) (particle) on a curve,  C,  in space .   Then      dr / dt     is a vector tangent to this curve. This curve, C, represents the path of motion of the particle, P,  in space.                        dr / dt     also represents the velocity of the particle along its path where     r   =  x i   +  y j  +  z k      where   i ,  j,  k    are unit vectors (base vectors) along axes    x, y, and z   fixed in space (using a rectangular, Cartesian description).   Here   x = x(t),   y = y(t),  and  z = z(t)       t  =  time   So         v   =   dr / dt     =    dx/dt i   +  dy/dt j  +  dz/dt k        where   dx/dt,   dy/dt,  and  dz/dt  represent the x, y, and z-components of velocity of the particle moving along C. 2 Acceleration of a particle in space – using “rectangular” Cartesian (x,y,z)  components   Acceleration of a particle is the time rate of change of its velocity,  v   =  dr / dt    .   So     a    =    dv / dt  .    In “rectangular coordinates”  x, y, z            a    =    dv / dt   =    d2x/dt2 i   +  d2y/dt2 j  +  d2z/dt2 k        Click here for further discussion.