Video Transcript
A spacecraft travels at a speed
of 5.5 kilometers per second. What is its speed in meters per
second?
Alright, so we have some
spacecraft. Let’s say that this is it. And we’re told that it’s moving
along at a speed of 5.5 kilometers per second. We’ll call that speed 𝑠. And we see it’s expressed in
units of kilometers, that’s the distance, per second, that’s the time. Just as a side note, this
agrees with our understanding of what speed is. It’s a distance divided by a
time. And here, we have kilometers, a
unit of distance, divided by seconds, a unit of time. So anyway, we have the speed 𝑠
in units of kilometers per second. But we want to express that
speed in a different set of units, in units of meters per second. So the basic question we want
to answer is how many meters per second is 5.5 kilometers per second.
Looking at the units involved
here, we can see that we won’t have to do anything to the units of time. We start out in units of
seconds. And we end up in those same
units. No conversion necessary
there. But we will need to convert the
distance from units of kilometers to units of meters. To do that, we can recall that
one kilometer of distance is equal to 1000 meters. Keeping that in mind, there’s a
mathematical operation we can perform on this original speed, 5.5 kilometers per
second, to convert it to the equivalent speed in units of meters per second.
To do this, we’re going to
multiply our original speed by one. Now, we’re not really going to
multiply by one exactly. But we are going to multiply by
something that is equivalent to one. And we’re going to choose that
something so that when we multiply it by our original speed, out come the units
that we want, meters per second. Here’s how we’ll do this. Recall that we want to convert
this distance unit, kilometers, to a unit of meters. And we’ve already recalled that
one kilometer is 1000 meters. Since that’s true since,
mathematically, the two values on either side of this equality are the same. That means if we write them as
a ratio, like we do here, then that ratio must be equal to one. That’s because the numerator,
1000 meters, is equal to the denominator. So this fraction is one.
But now, let’s think of what
happens when we multiply this fraction by our original speed. If we just focus on the units
for a moment, we have in the numerator units of kilometers times meters. And in the denominator, we have
units of seconds times kilometers. Since that factor of kilometers
appears in both the numerator and denominator once, that means it cancels
out. Once they’re gone, look at what
we have left over, units of meters per second, just the units we wanted to end
up with.
So by multiplying our original
speed by this ratio, even though the ratio is equal to one, it’s effected the
change in units that we wanted to bring about. When we multiply these two
values together, the result has units of meters per second. Knowing that, all we need to
figure out now is the number that goes in front of the units. And that number is equal to 5.5
multiplied by 1000. And that’s equal to 5500. So then, 5.5 kilometers per
second is equal to a speed of 5500 meters per second.
