Position simply tells you **the location of an object**.

What are the proper SI units to use for measurements of position?

meters (m)

Scientists often use the letters **x** and **y** to denote
the position of an object.
We'll deal with one-dimensional motion this week,
so we'll usually stick with **x**;
but when we reach two-dimensional motion,
we'll use **y**, too.
In three dimensions, of course, we could use **x**, **y**, and **z**.

Example: a car drives along a street past a tree.

We measure the position of the car at various times. There are (at least) three ways to communicate our measurements to someone. One is to make a table of the results:

time | 0 s | 1 s | 2 s | 3 s | 4 s |

position | 30 m | 35 m | 40 m | 45 m | 50 m |

Another way to describe the motion is to make a graph. We'll be doing this a lot.

A third way to describe motion is by writing a mathematical equation
which shows the position **x** as a function of time **t**.
How can we do that?
Well, let's look at how the position changes over time.
For example, between **t = 0 s** and **t = 1 s **,
we see

So, the ratio of "change in position" to "change in time" is

Physicists call this quantity **average velocity**.
It clearly must have the units of **meters per second**.
In this case, we see that

Okay, your turn.

Q: What is the average velocity of the car from t = 2 s to t = 4 s?

Right. It's still **v = 5 m/s**.
In fact, as far as our measurements go, the car has a constant velocity.
We can write an equation describing its position as a function
of time in this simple case like so, right?

time | 0 s | 1 s | 2 s | 3 s | 4 s |

position | 30 m | 35 m | 40 m | 45 m | 50 m |

No, that won't work. In order to force the equation to match the measurements, we need to add a constant distance.

Check this -- do all the terms end up with the same units? What are those units?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.