Here we see a *velocity vs. time graph*, or a
*v vs. t* graph.

Velocity (v) is *vertical*.

Time (t) is *horizontal*.

The object is moving at a *constant velocity* of
*6 m/s* as the time passes from *0 s*
to *6 s*.

Let's understand the *meaning of the area* of
this graph.

This is the *area under* this
*v vs. t* graph.

If we examine a section of this area, we notice that
*vertically* it is measured in units of *meters per second*.

We also notice that *horizontally* it is
measured in units of *seconds*.

The actual unit for the *area *will be units
of *meters per second times seconds*. This comes out to be
units of* meters*.

Here we see that along one edge of the area the
units are *meters per second*. Along the other edge the units
are *seconds*.

When values measured in these two units are
multiplied to find the area, the result has units of *meters
per second times seconds*. This results in a unit for **
***meters*.
The *seconds cancel*.

Therefore, this *area* is in units of **
***meters*.
It stands for *displacement*, or *change in position*,
which is measured in *meters*.

Here is the way an actual calculation for the
displacement of an object would proceed given this v vs. t
graph for the object's motion:

For the time period from 0 s to 6 s the
area under the v vs. t graph is a rectangle. This rectangle
is 6 m/s tall, and it is 6 s long.

Therefore, the area is equal to 6 m/s times
6 s, or 36 m.

36 m = (6 m/s)(6 s)

The displacement, or change in position,
for this object is 36 meters.

displacement = change in position =
delta x = Δx = 36
m

## The *area of the v vs. t graph* is the *change in position*, or the *displacement*.