Barrons AP Calculus

Velocity    vector

The velocity vector is the derivative of the vector function (the position
vector):

Alternative notations   for     and     are vx  and vy, respectively;   these   are the

components of v in the horizontal and vertical directions, respectively. The slope
of v is

,

which   is  the slope   of  the curve;  the magnitude   of  v   is  the vector’s    length:

.

Thus, if the vector v is drawn initiating at P, it will be tangent to the curve at P
and its magnitude will be the speed of the particle at P.