Motion

Part 1

Identify the quantities used to describe motion. Set up a coordinate system.

For The Interested Reader

If you want to talk about negative time or distance, you certainly can. It simply indicates a time or position prior to the starting coordinates.

For example, if I decide to start counting time from when I wake up at 6:00am, I would say that

If my cat woke me up at 5:30am I could say she woke me up at

And then I would have a word with my cat about respecting people's sleep schedules. ... ...

Which would go absolutely nowhere, because she's a cat.

There are two quantities necessary to talk about motion: distance (d) and time (t). From those two quantities, we will derive velocity (v) and acceleration (a).

Just so we don't get lost in abstract concepts, let's take a moment to think about these quantities in real-world terms.

• Distance: how far did we go?

• Time: how long did it take to get there?

• Velocity: how fast did we go?

• Acceleration: did our velocity change along the way?

Distance, d, is actually a change in position, x. We start at one position, , and end at a different position, . The change between these two positions is the distance.

Mathematically, we say that velocity is a derivative of position; acceleration is a derivative of velocity. For more information about derivatives, check out the Math Lessons section.

The equations for velocity and acceleration are:

Next, let's consider graphical representations of motion.

Standard Coordinate System

The standard coordinate system places the x-axis horizontally and the y-axis vertically, on the left:

The values on the x-axis increase to the right, and the values on the y-axis increase upwards. Typical physical quantities that would be graphed are position, speed and time. For now, we'll only talk about positive quantities. Later, we'll see that a negative sign has a significant meaning, such as a change in direction or slowing of speed.

Let's plot a change in position (or distance) versus time:

The above graph shows time as a function of position, or .

The slope of this graph is

or , which is velocity v.

Make sure to label both axes with appropriate quantities and units!