# Using Vectors to Describe Motion

Michael Fowler, University of Virginia

## Uniform Motion in a Straight Line

Let us consider first the simple case of a car moving at a steady speed down a straight road. Once we've agreed on the units we are using to measure speed -- such as miles per hour or meters per second, or whatever -- a simple number, such as 55 (mph), tells us all there is to say in describing steady speed motion. Well, actually, this is not quite all: it doesn't tell us which way (east or west, say) the car is moving. For some purposes, such as figuring gas consumption, this is irrelevant, but if the aim of the trip is to get somewhere, as opposed to just driving around, it is useful to know the direction as well as the speed.

To convey the direction as well as the speed, physicists make a distinction between two words that mean the same thing in everyday life: speed and velocity.

Speed, in physics jargon, keeps its ordinary meaning: it is simply a measure of how fast something's moving, and gives no clue about which direction it's moving in.

Velocity, on the other hand, in physics jargon includes direction. For motion along a straight line, velocity can be positive or negative. For a given situation, such as Charlottesville to Richmond, we have to agree beforehand that one particular direction, such as away from Charlottesville, counts as positive, so motion towards Charlottesville would then always be at a negative velocity (but, of course, a positive speed, since speed is always positive, or zero).