As in the one-dimensional case
we derive various diagnostics about motion in a plane. The
average velocity
is
points in the direction of the displacement
vector from the location of the particle at the beginning of the time
interval to the location of the particle at the end of the time interval.
Its magnitude however has dimensions of a velocity so in some sense
velocity vectors do not belong on a plot of the trajectory. It is ok
to put it there if we remember that strictly only the direction of the
velocity vector has meaning in such a representation.
We also define the instantaneous velocity much as in one dimension:
Because we can think of 
as the average velocity in a very small
time interval close to time t it follows from the previous discussion
that is parallel to the tangent of the trajectory at time t.
Here it is very easy to get mixed up with a graphical construction we
used when discussing velocity in one dimension. There we said that the
velocity equaled the slope of the tangent to the x(t) curve when
plotted in the x-t plane. Please be aware that these two constructions
are completely different and must not be confused!
The mathematical expression for the limit of Eq. 22
can be written
Thus the components of velocity along the 
and 
directions are related to the corresponding projections
of the position vector, x(t) and y(t), as is velocity to position
in one dimensional motion.
Finally remember that we also can talk about the speed of a particle. That is simply the magnitude of the velocity. When we ask for the average speed we mean the average magnitude of the instantaneous velocity. This means that if I drive to Disney World and back again my average speed might be 55 mph while my average velocity would in fact be zero because there was no net displacement over the time interval of the return trip.