Speed and Velocity: Concepts and Formulas

Speed and Velocity: Concepts

Did you know that speed and velocity are different? Most people consider speed and velocity to be the same and may even use these terms interchangeably. While speed and velocity are similar, they are definitely not the same. So how are they different? Speed is a matter of how fast an object is moving regardless of the direction it's going, whereas velocity is a matter of how fast an object gets somewhere with respect to direction. Think of a person repeatedly taking two steps forward and then two steps back. They are moving, but they're not getting anywhere. In other words, they have speed but no velocity. In short, speed is a measure of how fast an object moves, while velocity is a measure of how fast an object gets somewhere.

Definitions of Velocity and Speed

Before we discuss the formulas for calculating speed and velocity, we need to consider more detailed definitions of each term. Speed is defined as the rate of change in distance with respect to time. Velocity is defined as the rate of change in displacement with respect to time. Notice the words distance and displacement are the only difference between the two definitions.
So what's the difference between distance and displacement? Distance refers to the total amount of ground covered by an object in motion, whereas displacement refers to the net change in position of an object in motion. Distance is what we call a scalar quantity because distance is fully described by magnitude alone with no reference to direction. Since speed is a function of distance, speed is a scalar quantity as well. Displacement is a vector quantity because displacement is fully described with both magnitude and direction. Since velocity is a function of displacement, velocity is a vector quantity. If we combine the definitions of speed and velocity, one could say that velocity is speed with direction and that would be accurate.

Formula for Speed

Now that we understand the concepts of speed and velocity, we can examine the formulas for calculating these measures. Let's take a look at speed first. As discussed, speed is the rate of change in distance in a period of time. In other words, speed is a function of both distance and time. As such, the formula for calculating speed includes both distance and time, where speed is directly proportional to the change in distance and inversely proportional to the change in time.
Let's take a look at the formula for speed: Speed = distance ÷ time
Let's use an example to practice calculating speed. Consider a man walking in a zigzag pattern. If the man covers a total of 20 meters in the zigzag, then the change in distance is equal to 20 meters. Now let's say he takes 60 seconds to cover that 20-meter zigzag pattern. Therefore, the change in time is 60 seconds. We can put these values together in our formula and calculate for speed.
Let's first recall the formula for speed. Speed = distance ÷ time
Now plug in the observed values. Speed = 20 meters ÷ 60 seconds
20 divided by 60 equals 0.33. Therefore, the man is moving with a speed of 0.33 meters per second. This can be expressed as Speed = 0.33 m/sec where m = meters and sec = seconds. You may be more familiar with speed expressed as miles per hour, or simply MPH.

Formula for Velocity

Let's take a look at the formula for velocity. As we discussed, velocity is a measure of change in displacement over time, not just distance. In other words, velocity is a measure of how long it takes an object to reach a destination with direction. Velocity is directly proportional to displacement and inversely proportional to the time traveled.
Let's take a look at the velocity formula: Velocity = displacement ÷ time