Video: Speed

In this video, we will learn how to find speed as a rate of change of distance that objects move during a time interval.

07:54

Video Transcript

In this video, we’re going to be talking about speed. Now, speed is a measure of how fast something is moving. But in physics terms, we can be a bit more specific. How fast an object moves is basically another way of talking about how much distance that object covers or travels in a specific period of time.

In other words, if we think about a car moving in this direction and it moves a distance of 10 meters in a time interval of one second, then that car is said to have a higher speed, is said to move faster than a car that only moves say five meters in one second. So this is what speed is talking about. It’s the amount of distance covered by an object — in this case are cars — in a given amount of time.

More specifically, the speed of an object is defined as the distance covered by that object in a unit of time. So in this case, the unit of time that we’re using is one second. And so, we can say that the first car has a speed of 10 meters per second. It moves 10 meters every second. And the second car has a speed of five meters per second.

So using this understanding of what speed is, we can come up with a mathematical equation. We can say that the speed of an object is defined as the total distance moved by the object divided by the time taken to travel that distance.

Coming back to the case of our first car. We’ve been told that the car moves 10 meters. So that’s the total distance. And the total time taken is one second. Hence, we can say that the speed of the car is the total distance moved — that’s 10 meters — divided by the total time taken; that’s one second. And that ends up being 10 meters per second, just as we expected.

Now, it’s worth noting that we could have been told how far the car moves over a longer period of time. For example, we could have been told that the car travels a total distance of 20 meters and it takes a total time of two seconds to do that. So in this case, if we wanted to calculate its speed, we would say that it’s the total distance travelled — that’s 20 meters — divided by the total time taken — that’s two seconds. But then, 20 divided by two is 10. And so, the speed of the car is still 10 meters per second.

Therefore, we don’t necessarily have to be given the distance covered by our object in one unit of time because once again the unit of time we’re using is one second. However, we’ve been told how far the car travels in two seconds. But this is not a problem. We just use our equation here to give us the speed of the car. And of course, this only applies to a constant speed, so a speed that’s not changing over time.

But essentially, what a speed of 10 meters per second tells us is that every second the car is moving 10 meters. In other words, in the first second the car moves 10 meters and in the second second the car moves another 10 meters. Therefore, it moves a total distance of 20 meters in two seconds. Now, this equation that we’ve come up with is rather wordy. Let’s abbreviate all the terms slightly.

Let’s say that speed is represented by the lowercase letter 𝑠 and let’s say that the total distance moved by an object is represented by 𝑑 and the time taken to move that total distance is 𝑡. Putting it altogether, we’ve got the speed, distance, and time in an equation. And this is the relationship between speed, distance, and time.

Now, another way to word either this or this is to say that speed is the rate of change of distance moves because the words “rate of change” is talking about how much something changes over a given period of time. And so the rate of change of distance moved is simply the distance moved over a given period of time. Hence, the speed of an object is the rate of change of the distance moved by that object. So now that we’ve defined what speed is, let’s take a look at a couple of examples.

What is the speed of an object that travels a distance of 300 meters in a time of 25 seconds?

So in this case, we’ve got an object, which we’ll say for the purpose of our question is this round blobby thing. And we’ve been told that the object moves 300 meters. So let’s say it moves 300 meters in this direction, which means that it starts here and finishes here. And we’ve been told that it travels a distance of 300 meters in a time of 25 seconds. We need to work out the speed of this subject. So let’s start by providing labels to the 300 meters and 25 seconds.

Let’s say that the distance moved firstly is called 𝑑 and the time taken to travel that distance is called 𝑡. Then, we can recall the definition of speed. Speed is the rate of change of distance moved by an object. In other words, speed is equal to the distance moved by an object divided by the time taken to travel that distance.

And in this question, we’ve already been given the distance travelled by the object and the time taken to travel that distance. So we can work out the speed simply by substituting in our values of 𝑑 and 𝑡. So we can say that the speed of the object 𝑠 is equal to 300 meters — that’s the distance moved by the object — divided by 25 seconds — that’s the time taken for the object to move 300 meters.

And since we’ve kept our units in the calculation, we can see that our final answer is going to have the unit of meters per second or meters divided by seconds. And so, when we evaluate the right-hand side of this equation, we get our final answer which is that the speed of the object is 12 meters per second.

In other words, every second that object is travelling 12 meters. So the first second it travels 12 meters, the second second it travels another 12 meters, the third second it travels yet another 12 meters, and so on and so forth until 25 seconds later and it’s traveled the total distance of 300 meters. Hence, we say that it’s done this at a speed of 12 meters per second.

So now that we’ve seen this example, let’s look at another example which this time gives us the speed of the object, but we have to calculate another quantity.

How much time is taken for an object with a speed of 80 meters per second to travel a distance of 300 meters?

So in this question, we’ve been told that we’ve got an object — let’s say this blob is our object — and it’s moving at 80 meters per second. So let’s say it’s moving towards the right at 80 meters per second. We’ve been told that this objective is moving a distance of 300 meters. So from its start point to its finish point, the distance the object moves is 300 meters. And we’ve been asked to calculate the amount of time taken for this subject to travel that distance.

So let’s start by saying that the distance moved by the object is called 𝑑 and the speed with which the object moves is called 𝑠. Now that we’ve done this, we can recall that the speed of an object is defined as the total distance travelled by the object divided by the time taken for that object to travel that distance. Or in other words, speed is the rate of change of the distance moved by the object, where rate of change simply means how much something is changing over a given period of time. In this case, we’re talking about the rate of change of the distance moved, so how much distance the object is moving over a given period of time.

Now in this question, we’ve already been given the speed of the object and the distance moved by the object. However, we’ve been asked to calculate how long it takes to do that. So what we need to do is to rearrange this equation here. We need to do this so we can solve for 𝑡. We can do this by multiplying both sides of the equation by 𝑡 divided by 𝑠.

This way, on the left-hand side of the equation, the 𝑠 in the denominator cancels with the 𝑠 up top. And similarly, on the right-hand side, the 𝑡 in the numerator cancels with the 𝑡 in the denominator. Well that leaves us with 𝑠𝑡 on the left-hand side and 𝑑 divided by 𝑠 on the right. So when we clean things up a bit, we can see this a bit more clearly: the amount of time taken for an object to move a certain distance is equal to that distance moved divided by the speed of the object.

Now at this point, we can substitute in the values. So we can say that the time taken for the object to move the distance is the distance 300 meters divided by the speed of the object 80 meters per second. Looking very quickly at the units, we can see that we’ve got meters in the numerator and a meters in the denominator. So these will cancel. And what we’re left with is one divided by seconds in the denominator which is equivalent to having seconds in the numerator.

And hence, our final answer is going to have the unit of seconds, which is exactly what we want because we’re trying to find the value of time. And the unit of time is seconds. So when we do evaluate the fraction on the right-hand side, we get an answer of 3.75 seconds. That’s the amount of time taken for the object to move a distance of 300 meters at a speed of 80 meters per second.

Okay, so now that we’ve had a look at a couple of examples, let’s summarize what we’ve talked about in this lesson. We saw in this lesson that speed is the rate of change of distance moved by an object. In other words, we can say that the speed of an object is the total distance moved by the object divided by the time taken to move that distance.

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