Question Video: Converting from Kilometers per Hour to Meters per Second Physics

What value of speed in kilometers per hour is equal to a value of speed of one meter per second?


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 𝑠 is equal to a distance 𝑑 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.

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