 In the limit as the time interval Δ"t" becomes smaller and smaller, the average velocity becomes the time derivative of the position vector,
Thus, velocity is the time rate of change of position of a point, and the dot denotes the derivative of those functions x, y, and z with respect to time.Furthermore, the velocity is tangent to the trajectory of the particle at every position the particle occupies along its path.Note that in a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants.