#### Velocity Vectors

The velocity at any point in time is:

**v** = **v**_{o} + **a**t

Taking up to be positive **a** = -g and **v** = **v**_{o} + (**-gt**)

g is just the magnitude of the acceleration due to gravity.

As time goes by **v**_{o} is constant and **-gt** grows linearly with time, so the velocity **v** changes at a constant rate.

Another way to look at this is to use **v**_{2} = **v**_{1} + Δ**v**.

When the acceleration is constant Δ**v** = **a** Δt.

So, **v**_{2} = **v**_{1} + (**-g Δt**).

By stepping the motion forward in equal time steps you can see that the change in velocity is the same for each step.