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Lesson Video: Velocity Science

In this video, we will learn how to distinguish between the speed and the velocity at which an object moves between two points.

09:29

Video Transcript

In this video, we will learn how to distinguish between the speed and the velocity at which an object moves between points. To get started, imagine we have an object and that this object moves along a curved path. The object ends up here, and we can say the distance the object traveled is the length of this curved arc. On the other hand, if we drew in the object’s displacement, that would look like this.

Notice that displacement is a vector. The direction of the arrow shows us the overall direction of object motion. We also see that displacement is measured as a straight-line distance between a starting and ending position. Displacement and distance are quite different from one another. That difference is important when we talk about the speed of this object compared to its velocity. Object speed is defined as a distance traveled divided by the time taken to travel that distance. Just as distance is a scalar quantity, so is speed. Velocity is different. It’s equal to displacement divided by time. And since displacement is a vector, velocity is too.

We can now compare the speed of this object to its velocity. When we figure out its speed, the amount of time we would use would be equal to the amount of time we would use to figure out its velocity. Therefore, the difference between this object’s velocity and speed comes down to the differences between its displacement and distance traveled. Because our object is following a curved path, the distance that it travels is greater than the magnitude of displacement. In this particular case then, we can say that our object’s speed is greater than the magnitude of its velocity.

And then, as we said, another difference between speed and velocity is that velocity is a vector. Speed, which depends on distance and time, is a scalar quantity. Whenever a moving object follows a curved path, like our object does here, this statement will be true. The object’s speed will always be greater than the magnitude of its velocity. On the other hand, if we have an object that moves in a straight line, then the distance traveled by the object will equal the magnitude of its displacement. For a straight-line path where an object never changes direction, speed is equal to the magnitude of velocity. This is so because, as before, the time we used to calculate these two terms is the same. Knowing all this about speed and velocity, let’s look at some examples.

Two aircraft fly along the path shown, each flying for the same amount of time. Which color arrow shows the path of the aircraft with greater speed? (A) The blue arrow, (B) the green arrow, (C) the speeds are the same.

In our diagram, we see these two moving aircraft. The one following the blue arrows moves like this, and the aircraft following the green arrow like this. To determine which aircraft has the greater speed, let’s recall that, in general, the speed of an object equals the distance that object travels divided by the time taken to cover that distance. In our question, we’re told that each of these aircraft flies for the same amount of time. This means the aircraft with the greater speed will be the one that travels the greater overall distance.

Our diagram shows us that each aircraft moves up and to the right the same amount. This means we can take this green arrow and slide it on top of the blue arrows, and it will look like this. It now becomes clear which arrow involves the greater distance between the initial and final positions. The distance covered by the green arrow is less than the distance covered by the two blue arrows. Since the blue arrow distance is greater, so is the speed of the plane following this arrow. We choose answer (A). The blue arrow shows the path of the aircraft with greater speed.

Let’s look at another example.

If an object moves in a straight line at a uniform speed, which of the following is correct? (A) The speed becomes a vector quantity. (B) The speed is the magnitude of the velocity of the object.

Let’s say that here is our object and that this is its path of motion. Traveling at a uniform or constant speed, the object ends up here. So this is the distance the object travels, while this arrow shows the object’s displacement. Because our object has moved in a straight line, the distance and the magnitude of the displacement, the length of this arrow, are the same. Mathematically, we can write that this way. Distance equals the magnitude of displacement.

Now, our second answer option, option (B), talks about the speed of the object as well as its velocity. We can recall general equations for speed and for velocity. The speed of an object equals the distance it travels divided by the time taken to cover that distance, while velocity, a vector quantity, equals displacement divided by time. In this equation for velocity, if we took the magnitude of displacement, then on the left-hand side we would have the magnitude of velocity. And now let’s recall that in our particular scenario, with our object moving in a straight line at a constant speed, the distance the object travels is indeed equal to the magnitude of its displacement.

Looking at our equations, that means we can say the magnitude of displacement here equals this distance here. Going further, for our object moving in a straight line, the time used to calculate speed is equal to the time used to calculate the magnitude of velocity. We can therefore write that our object’s speed is equal to the magnitude of its velocity. This corresponds to answer option (B). Note that option (A) can’t be correct because speed is always a scalar, not a vector, quantity. For an object moving in a straight line at a uniform speed, the speed of the object equals the magnitude of the object’s velocity.

Let’s look now at another example.

Two aircraft fly along the paths shown, each flying for the same amount of time. Which color arrow shows the path of the aircraft that flies between its initial and final positions at the greater velocity? (A) The blue arrow, (B) the green arrow, (C) the velocities are the same.

Comparing these two aircraft, we see they each travel between an initial and a final position that are separated by the same amount of vertical and horizontal distance. We want to know which one travels between the initial and final positions at the greater velocity. Let’s remember a general equation for velocity. It’s equal to an object’s displacement divided by the time taken to be displaced some amount. The fact that we’re considering displacement is key.

Displacement, we recall, only takes into consideration the start and endpoints of an object’s motion. So the displacement of the plane following the green arrow is given by this arrow, and the displacement of the plane following the blue arrows is given by this arrow. These displacements are the same. And since the planes both flew for the same amount of time between their initial and final positions, we can say that since each plane had the same displacement and the same amount of time elapsed, the velocities of both aircraft are the same. As a side note, the speeds of these aircraft are not the same. But since velocity depends on displacement and both planes have the same displacement, their velocities are indeed equal.

Let’s look now at one last example.

An aircraft follows the curved line shown. Which has the greater magnitude, the aircraft’s speed or its velocity? (A) Speed, (B) velocity.

Let’s begin by thinking about the general difference between speed and velocity. Speed equals the distance an object travels divided by the time taken to cover that distance. Our aircraft covers a distance equal to the length of the curved line. If we divide this distance by the time it takes for the aircraft to move from its initial to its final position, we get the aircraft’s speed. Velocity, on the other hand, is equal to an object’s displacement divided by time.

Displacement can be different from distance in two ways. First, displacement is a vector, while distance is a scalar. Second, the magnitude of an object’s displacement is equal to the straight-line distance between that moving object’s initial and final positions. In other words, this pink arrow represents our aircraft’s displacement. In this question, we’re to compare the magnitude of our aircraft’s speed with the magnitude of its velocity. The magnitude of an object’s velocity in general equals the magnitude of its displacement over time. For our aircraft, the magnitude of its displacement is equal simply to the length of this pink arrow.

Now, here’s the question. Which is greater, the magnitude of this displacement or this distance along the curved path? We can tell that the distance is greater. And that means that our aircraft’s speed is greater than the magnitude of its velocity. By the way, this is always true when an object moves along a curved path. For our answer, we choose option (A).

Let’s now finish our lesson by summarizing a few key points. In this video, we saw that speed is a scalar quantity. Written as an equation, speed equals distance divided by time. In contrast, velocity is a vector quantity. Written as an equation, velocity equals displacement divided by time. This is a summary of velocity.

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