Average Acceleration and Instantaneous Acceleration

When a particle's velocity changes from to in a time interval , its average acceleration during is

Or

If we shrink to zero about some instant, then in the limit approaches the instantaneous acceleration (or acceleration) at that instant; that is,

(4-16)

If the velocity changes in either magnitude or direction (or both), the particle must have an acceleration.

We can write Eq. 4-16 in unit-vector form by substituting for v*from Eq. 4-11 to obtain

We can rewrite this as

(4-17)

where the scalar components of are

(4-18)

We can rewrite this as

(4-17)

where the scalar components of are

, (4-18)