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CLEP Natural Sciences: Study Guide & Test Prep25 chapters | 277 lessons

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Lesson Transcript

Instructor:
*John Simmons*

John has taught college science courses face-to-face and online since 1994 and has a doctorate in physiology.

Did you know that an object's speed and velocity may not be the same? This lesson describes the concepts of speed and velocity relating to objects in motion. We'll look at a specific example to help learn how to calculate both speed and velocity.

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.

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.

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**.

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**

Let's consider once again that man traveling in the zigzag pattern. We determined his speed to be 0.33 meters per second. We know his speed, but what about his velocity? In order to calculate velocity, we must first determine displacement. To determine displacement, measure the distance in a straight line from the man's starting point to his destination. Now, let's say we measure that displacement to be 5 meters to the right. Now, we can calculate for velocity.

Let's first recall the formula for velocity: **Velocity = displacement ÷ time**

Plug in the measured values for displacement and time and we get velocity = 5 meters to the right ÷ 60 seconds.

Now, 5 divided by 60 is 0.08. Therefore, the man's velocity is 0.08 meters per second to the right. Once again, velocity is a vector quantity expressing both magnitude and direction. Here, the magnitude is 0.08 and the direction is to the right.

To summarize, speed and velocity are similar but different. **Speed** is a measure of distance traveled over time, where **distance** refers to how much ground is covered by an object in motion. **Velocity** is a measure of displacement over time, and **displacement** refers to the net change in position of an object in motion. Distance and speed are **scalar quantities**, as they are fully described by magnitude with no reference to direction. Displacement and velocity, on the other hand, are **vector quantities**, as they are fully described by both magnitude and direction. **Velocity** can be thought of as speed with direction. The formula for speed is change in distance divided by change in time. The formula for velocity is change in displacement divided by change in time.

Following this video lesson, you'll be able to:

- Differentiate between speed and velocity
- Write the equations for both speed and velocity

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CLEP Natural Sciences: Study Guide & Test Prep25 chapters | 277 lessons

- Speed and Velocity: Concepts and Formulas 6:44
- Implications of Mechanics on Objects 6:53
- Newton's First Law of Motion: Examples of the Effect of Force on Motion 8:25
- Newton's Second Law of Motion: The Relationship Between Force and Acceleration 8:04
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