# Slope of the x vs. t Graph, Velocity

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Here is an *x vs. t*, or *position vs. time*, graph.

Position (x) is *vertical*.

Time (t) is *horizontal*.

Initially, when *t = 0 s*, the object is at **
***x = 0 m*.

From then on as time passes the object moves away from the origin of the position
(x) number line.

Let's look at two points on this graph....

Examine the *first* point, *(t*_{1}*, x*_{1}).

When *t*_{1}* = 5 s*, then
*x*_{1}* = 15 m*.

Examine the *second* point, (t_{2}, x_{2}).

When *t*_{2}* = 15 s*, then
*x*_{2}* = 45 m*.

Let's find the *slope* of this graph using those two points...

Using those two points, here is the *rise* and the
*run* of the *slope* of this
*x vs. t* graph.

Here, the *rise* is the *difference of the position* coordinates, or
*x*_{2}* - x*_{1}, as in:

rise = x_{2} - x_{1}

rise = 45 m - 15 m

rise = 30 m

Here, the *run* is the *difference of the time* coordinates, or
*t*_{2}* - t*_{1}, as in:

run = t_{2} - t_{1}

run = 15 s - 5 s

run = 10 s

The *slope* of this graph is **
***a change in position divided by a change in time*, as in:

slope = rise / run

slope = 30 m / 10 s

slope = 3 m/s

This * ***slope is
the velocity** of the object, since
*velocity* is *defined* as the
*change in position divided by the change in time*.
So....

Velocity = 3 m/s.

## The *slope of the x vs. t* graph is the *velocity* of the object.

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