### 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.