At any time t, the location of the object is at some point (x,y,z).


We can specify the position of the object by three functions:

    The position at time t is (f(t), g(t), h(t) ).


Now if we want to find out the velocity of the particle, we

take the distance it goes divided by the time.


       Distance from (f(t),g(t),h(t)) to (f(t+dt),g(t+dt),h(t+dt)
       -----------------------------------------------------------
                                 dt

Or, using the distance formula

                        2                   2                  2
   Sqrt[  (f(t+dt)-f(t))   + ( g(t+dt)-f(t))   + (h(t+dt)-h(t))   ]
  -------------------------------------------------------------------
                            dt
          
        _                                                               _
       |   _                _  2   _            _ 2    _            _ 2  |
       |  |                  |    |              |    |              |   |
       |  | f(t+dt)-f(t)     |    | g(t+dt)-g(t) |    | h(t+dt)-h(t) |   |
   Sqrt|  | --------------   |  + |------------- |  + | ------------ |   |
       |  |_     dt         _|    |_     dt     _|    |_            _|   |
       |_                                                               _|


    And taking the limit we get

            
          Sqrt[ f'(t)^2 + g'(t)^2 + h'(t)^2 ]