Velocity: Speed and direction.

You are familiar with the concept of speed. It tells you how fast something is going: 55 miles per hour (mi/h) is an example of speed. The speedometer in a car measures speed but does not indicate direction.

When you need to know both speed and direction, you use velocity. Velocity is a vector. It is the measure of how fast and in which direction the motion is occurring. It is represented by v. In this section, we focus on average velocity, which is represented by v with a bar over it, as shown in Equation 1.

A police officer uses the concepts of both speed and velocity in her work. She might issue a ticket to a motorist for driving 36 mi/h (58 km/h) in a school zone; in this case, speed matters but direction is irrelevant. In another situation, she might be told that a suspect is fleeing north on I-405 at 90 mi/h (149 km/h); now velocity is important because it tells her both how fast and in what direction.

To calculate an object’s average velocity, divide its displacement by the time it takes to move that displacement. This time is called the elapsed time, and is represented by Δt. The direction for velocity is the same as for the displacement.

For instance, let’s say a car moves positive 50 mi (80 km) between the hours of 1 P.M. and 3 P.M. Its displacement is positive 50 mi, and two hours elapse as it moves that distance. The car’s average velocity equals +50 miles divided by two hours, or +25 mi/h (+40 km/h). Note that the direction is positive because the displacement was positive. If the displacement were negative, then the velocity would also be negative.

At this point in the discussion, we are intentionally ignoring any variations in the car’s velocity. Perhaps the car moves at constant speed, or maybe it moves faster at certain times and then slower at others. All we can conclude from the information above is that the car’s average velocity is +25 mi/h.

Velocity has the dimensions of length divided by time; the units are meters per second (m/s).