Video Transcript
A car is traveling at a speed of 40 kilometers per hour. What is the speed of the car in meters per second? Answer to the nearest meter per second.
So in this question, we are given the speed of a car in units of kilometers per hour and we are asked to work out the value of this speed in units of meters per second. Okay, so we have our car and we know that it’s traveling at a speed of 40 kilometers per hour. We’ve been asked to take this speed of 40 kilometers per hour and express it in units of meters per second. At the moment, we don’t know the numerical value of the speed in these units. So for now, we’re calling that value 𝑥. Our task in answering this question is then to find the numerical value of 𝑥.
In order to do this, we’ll need to recall the conversion between kilometers and meters and also the conversion between hours and seconds. We’ll start by recalling that one kilometer is equal to 1000 meters, since the prefix “kilo-” or K means 1000. For the conversion between hours and seconds, we need to recall that there are 60 minutes in one hour and that there are 60 seconds in one minute. So then we can write one hour as one hour multiplied by 60 minutes per hour multiplied by 60 seconds per minute. Looking at the units on the right-hand side of this expression, we could say that we can cancel the hours with the per hour and the minutes with the per minute, which means that on the right-hand side of this expression, we are left with units of seconds.
If we do the multiplication, we have that 60 multiplied by 60 gives us 3600. And so we can say that one hour is equal to 3600 seconds. So we have now successfully found the conversion between kilometers and meters and the conversion between hours and seconds. So if we start with our speed of 40 kilometers per hour, then we can use this relation here to replace the kilometers by 1000 meters and this relation to replace the hours by 3600 seconds. When we do this, we get that 40 kilometers per hour is equal to 40 multiplied by 1000 meters divided by 3600 seconds.
Once we separate out the numerical values and the units, we see that this is starting to look like the right-hand side of our expression up here. And so we can see that this numerical value here is the value of 𝑥 that we said we were trying to find. When we evaluate this number, we get a result of 11.1 recurring, where we have placed a bar over the one to indicate that this digit recurs. Looking at this relation here, we see that we have successfully expressed the speed of 40 kilometers per hour in units of meters per second.
But if we now have a look back at the question, we see that we were asked to give our answer to the nearest meter per second. This means that we need to take our result in units of meters per second and round this result to the nearest whole number of meters per second. When we round our value of 11.1 recurring to the nearest meter per second, we get 11. And so, we have our answer to the question that the speed of the car, measured in meters per second, is equal to 11 meters per second.
