**Previous section: ****Basic Kinematic Models of Particle Motion****.**

__Next section__**: ****Constant Acceleration Model****.**

Sketch a motion map for the algebraic model: **x**(*t*) = **x**_{0} + **v***t*

[Note that including the origin or coordinates in the map introduces arbitrary and unnecessary complications.]

This is really the same equation as the parametric equation in exercise (2) of __High School Geometry with GA__

for a straight line, **x**(α)** **= **a **+ α**u**. We've just used *t* (for time) as our parameter name here and changed the names

of the constant vectors. The link to **Solutions** for the exercises on that page shows an interactive diagram.

Derive a nonparametric equation for this model, and relate it to angular momentum.

Again, we could refer to the link mentioned in the previous paragraph, where the exercises started with a

nonparametric equation. We can get back to that kind of form by wedging our equation above on both

sides by the constant velocity **v**. But, we may as well wedge with *m***v** so that we see the relationship to

angular momentum:

**x**(*t*)**∧**(*m***v**) = **x**_{0}**∧**(*m***v**)

That is, the angular momentum of the free particle at any time is a bivector with the same orientation and

value as the initial angular momentum bivector. These bivectors can also be seen as the blue and green

bivectors in the interactive diagram referred to above, where the diagram's vector **a** is replaced by our **x**_{0}

and the diagram's vector **u** is replaced with *m***v**.

__Previous section__**: ****Basic Kinematic Models of Particle Motion****.**

**Next section: ****Constant Acceleration Model****.**