Basic Physics:  Speed and Velocity

Physics is a VERY broad subject.  Phenomena that physics can describe range from describing how and why a baseball flies from my hand to your glove, the sound the ball makes when it hits the glove, why the glove warms up a little when you catch the ball, how the temperature of the air effects the flight of the ball, and even how the electrons of one of the atoms in a molecule of the core of the ball interact and so on.

A traditional place to start learning physics is with motion:  describing motion (kinematics) and explaining motion (dynamics).  To begin describing motion, let's consider the following scenario.  You are standing in a large, open parking lot.  You see a friend driving their car into the parking lot.  Consider all the questions you could ask to describe the motion of your friends car.

Here are some possible questions:

How fast is the car going?

Which direction is the car going?

Is the car speeding up?

Is the car slowing down?

Is the car turning?

The figure below arranges these questions graphically.

In physics, as in all science, terms have very specific meanings.  How fast something is going is referred to as speed.  Speeding up is referred to as acceleration.  This is not any different than everyday language.  What does differ a bit is the fact that in physics, slowing down and even turning at a constant speed are referred to as acceleration.

The figure above is shown with some additional terms and graphics.

First consider constant speed.  From the diagram, we see that this is in the upper left quadrant:  speed, constant and how fast is the car going.  For most American's, mentioning the speed of a car brings to mind the units:  miles per hour.  In the metric system, the system of measurement used in physics, the standard unit of speed is:  meters per second.  Now, if the car in this example were traveling at 30 miles per hour, we all have a pretty good sense of how fast this is, but what does it literally mean?  At this speed, a car would travel 30 miles in one hour.  This gives us a hint about the equation for speed.  Speed is distance traveled divided by the time it took to travel that distance.  In mathematical form, this is:

and using variables to represent the words:  .  To make matters a little confusing, most physics books represent speed with the variable v rather than s.

We'll find out why shortly.

Exercise 1.  How do you convert 30 miles per hour into m/s?

We need to know how many meters there are in one mile and how many seconds there are in an hour.

1.0  miles = 1.6 km                    1.0 km = 1000 m

1.0 hours = 60 minutes 1.0 min = 60 s

The algebraic relationship between v, d and t that defines speed, allows one to calculate for any one of the variables, provided you have values for the other two.

Looking at the top of the motion diagram, you observe that the word velocity involves speed and direction.  It's actually that simple:  speed in a given direction is called velocity.  For example:  30 mph is a speed.  30 mph East is a velocity.  We refer to mathematical quantities that have both a numerical value and a direction as vectors.  A mathematical quantity that has a numerical value but no direction is called a scalar.

Is speed a scalar or a vector quantity?

Is velocity a scalar or vector quantity?

To symbolize vector quantities, we place a small arrow over the variable.  For velocity, the symbol is:    Thus, using the previous example, one could write:

Going back to the motion diagram, you will notice that both speed and velocity are in the �constant� region.  We know that the speed and the direction of a moving car can both change.  When the speed, the direction, or both the speed and direction of a moving car change, we call this acceleration.  The numerical quantity we actually measure for acceleration is the rate at which speed or direction changes.