Video Transcript
What value of speed in
kilometers per hour is equal to a value of speed of one meter per second?
Okay, so this example is
telling us that we have a speed of one meter per second. And if we recall the fact that,
in general, speed đť‘ is equal to a distance đť‘‘ divided by the time it takes to
travel that distance 𝑡, then we can see that indeed this number, one meter per
second, is a speed. It’s a distance over a
time. What we want to do is express
this speed in a different set of units, in units of kilometers per hour. The question we want to answer
is how many kilometers per hour is one meter per second. What we’re doing is converting
a speed in one set of units to its equivalent speed in another set. That is, the actual speed of
whatever is in motion isn’t changing. Only the units in which we
express that speed are changing.
To write this one meter per
second speed in units of kilometers per hour, we’ll need to make two
conversions. First, we’ll need to convert
meters to kilometers. And then, we’ll need to convert
seconds to hours. To get a start at doing this,
let’s recall that one kilometer is equal to 1000 meters. In order to reexpress the
distance unit in our speed of one meter per second, in units of kilometers,
we’re going to multiply this speed by a particularly chosen fraction. There are two requirements that
this fraction needs to satisfy. First, the numerator needs to
be equal to the denominator. In other words, the fraction
overall must be equal to one. The second requirement is that,
by multiplying by this fraction, our original speed must then have its speed
expressed in kilometers per second, rather than meters per second.
Using our conversion between
kilometers and meters, we can write out a fraction that fits both these
requirements. Here’s what we’ll do. Keeping in mind that we want
this unit of distance to cancel out and be replaced by a unit of kilometers,
we’ll put the distance of 1000 meters in the denominator of our fraction. In the numerator, we’ll put one
kilometer. After all, one kilometer is
equal to 1000 meters. That means this fraction we’ve
created does equal one, which is one of the conditions we had for it. But then, see how it meets our
second condition too. If we multiply this fraction by
the original speed, then the units of meters cancel out from numerator and
denominator. The remaining units are
kilometers up top and seconds down bottom. At this point, if we multiply
these two values together, we’ll get a result in units of kilometers per
second.
Now we’re headed in the right
direction. That would give us a result
with distance units in kilometers like we want. But recall that we also need to
convert the time units, from seconds to hours. To start doing that, we can
recall that one hour is equal to 3600 seconds. And the reason an hour is 3600
seconds is because one hour is made of 60 minutes. And each minute has 60 seconds
in it. And 60 times 60 is 3600. Now that we’re working on
converting our unit of time, seconds, into units of hours, we’ll once again
multiply our originally given speed by a fraction, which must be equal to one
but will give us the units in time that we want, hours.
Using our conversion between
hours and seconds, the numerator of this fraction is 3600 seconds. And the denominator is one
hour. Since one hour is equal to 3600
seconds, this fraction is equal to one. But looking at the units, we
see that when we multiply this fraction by our original value, the time units of
seconds cancel out with one another. And we’re left with one over
hours. Now that we’ve cleared away all
the cancelled out units, see what’s left. What remains is a speed in
units of kilometers per hour, just like we wanted. To figure out what that value
in kilometers per hour is, we’ll multiply our original speed times one over 1000
times 3600. The result of all that is
3.6.
So then, a speed of one meter
per second is equal to 3.6 kilometers per hour.
