Question Video: Converting Between Different Units of Speed Physics

Video Transcript

What value of speed in meters per second is equal to a speed of one kilometer per hour? Answer to three decimal places.

This question is asking us to convert a speed measured in units of kilometers per hour into a speed measured in units of meters per second. We are told that the speed is equal to one kilometer per hour. We can say that the speed of one kilometer per hour is equal to some value in units of meters per second. At the moment, we don’t know what that value is; so, for now, we’ve called it 𝑥. And our job in answering this question is to find out what the value of 𝑥 actually is. In order to do this, we’re going to have to recall the conversion between kilometers and meters and also the conversion between hours and seconds.

We can start by recalling that one kilometer is equal to 1000 meters, since the prefix kilo-, or k, means 1000. So that’s the conversion between kilometers and meters. Now, we just need the conversion between hours and seconds. Now, there are 60 minutes in one hour and 60 seconds in one minute. So, we can write that one hour is equal to one hour multiplied by 60 minutes per hour multiplied by 60 seconds per minute. If we look at the units on the right-hand side of this, we have the hours canceling with the per hour and the minutes canceling with the per minute. This leaves us with a conversion between hours on the left-hand side and seconds on the right-hand side. If we do the multiplication, we find that 60 multiplied by 60 gives us 3600. So, we have that one hour equals 3600 seconds.

We have now also found the conversion between hours and seconds. So, we can take our speed of one kilometer per hour. And we can use this expression here to replace kilometers by 1000 meters. And likewise, we can use this expression to replace per hour by per 3600 seconds. On the right-hand side of this equation, we can group all of the numbers together and all of the units together, giving us 1000 divided by 3600 meters per second. We have found that one kilometer per hour is equal to 1000 divided by 3600 in units of meters per second. When we evaluate this fraction, we find a result of 0.27 recurring, where we’ve drawn a bar over the seven to indicate that this digit is recurring.

So, we now have a result for our speed of one kilometer per hour in units of meters per second. But if we look back at the question, we see that we were asked to give our answer to three decimal places. Now, 0.27 recurring is just 0.2 followed by sevens that will go on indefinitely. Since we’re asked for an answer to three decimal places, we know that we need to stop this infinite number of sevens at this point here. Since our fourth decimal place is a seven, then our third decimal place will round up. And so, we have our answer that, to three decimal places, one kilometer per hour is equal to 0.278 meters per second.