#### Velocity Vectors

The velocity at any time is: **v** = **v**_{o} + **a**t

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

g is the magnitude of the acceleration due to gravity.

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

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

When the acceleration is constant **Δv** = **a** Δt= -**g**Δt.

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

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