A *velocity vector* is first and foremost a vector. That is, it has both a magnitude and a direction. I will not discuss vectors here; that will be left up to the *vector* node. Suffice it to say that, in Cartesian coordinates, a *velocity vector* can be written as a set of components. A 3-dimensional velocity vector, **v** can be written in the form of <vx, vy, vz>.

The *velocity vector* is a vector which represents the velocity of an object. The velocity of an object is simply *the distance travelled by the object per unit time.* As stated, this is only a magnitude, but velocity is in reality directional in nature. More precisely stated, a velocity is *the time derivative of the positional function of the object.* That is, it is the change in the position of the object per unit time. Thus, if supplied a function which gives the position, **r** of an object at any given point in time, say <rx, ry, rz>, the *velocity* can be determined by:

- vx = d/dt(rx)
- vy = d/dt(ry)
- vz = d/dt(rz)

More

generally stated,

*vi = d/dt(ri)*, where ri and vi are the

magnitude of

**r** and

**v** vectors,

respectively, in the

direction the i-

axis. For example, for vx and rx, i = 1. For vy and ry, i = 2. Because of the

componentwise

nature of the

vector derivative, the above can be written more simply as:

**v** = d/dt(

**r**).

Naturally, then, **r** can be determined by integrating each component of **v**. The acceleration vector, **a** is just the time derivative of **v**, and thus **v** can be found by integrating **v**. A quick overview:

I | acceleration /\
N | |
T | | D
E | | E
G | velocity | R
R | | I
A | | V
T | | E
E \/ position |

Although not

necessarily apparent,

velocity is a

vector, and thus, a

*velocity vector* is simply a

vector which

stores a

velocity. The

velocity is not in the

vector itself; it's in the

use or

interpretation of the

vector.