Most important is the instantaneous acceleration:
The direction of the acceleration is that of the change in velocity over a
small time interval around the time t. There is a completely new
type of motion which can occur in two dimensions but not in one dimension.
In one dimension acceleration is always associated with a changing magnitude
of the velocity. In two dimensions it is possible to change the orientation
of the velocity vector without changing its magnitude. This type of motion
is also motion with a finite acceleration. Uniform
circular motion is a particularly
simple example of this which we shall learn more about tomorrow.
Again the limits in Eq. 26 can be written as derivatives:
