This definition implies thatAcceleration is the rate of change of velocity with time.

where is the body's acceleration at time , and is the change in velocity of the body between times and .

How should we choose the
time interval
appearing in Eq. (15)? Again, in the
simple case in which the
body is moving with *constant* acceleration, we can make
as
large or small as we like, and it will not affect the value of . Suppose, however,
that is constantly changing in time, as is generally the case.
In this situation,
must be kept sufficiently small that the body's acceleration
does not change appreciably between times and
.

A general expression for instantaneous acceleration, which
is valid irrespective of how rapidly or slowly the body's acceleration changes in time,
can be obtained by taking the limit of Eq. (15) as
approaches
zero:

(17) |

Fortunately, it is generally not necessary to evaluate the rate of change of acceleration with time, since this quantity does not appear in Newton's laws of motion.