The velocity vector is a tangent to the trajectory. This allows us to draw
at times separated by a small time interval 
.
(see Fig. 3-21 (b) in Fishbane et al.)
We see that
W divide this equation by the corresponding time interval, to
get
Finally we take the limit of this expression as 
to obtain
From the sketch we also see that the direction of 
is towards
the center so that we can write
Where 
is the unit vector pointing in the same direction
as the position vector 
of the particle.
This acceleration is called the centripetal acceleration. It is the
acceleration which is required to keep a particle in uniform circular
motion.