Video Transcript
What value of speed in meters per second is equal to a speed of one mile per hour? Round your answer to two decimal places.
Here, we’re starting with a value of one mile per hour. So we have distance units of miles and time units of hours. And we want to convert this to a value with a distance unit of meters and a time unit of seconds. Solving this will require two steps. We’ll take our value of one mile per hour. And first of all, we’ll multiply it by a fraction that will convert the unit distance from miles to meters. And then we’ll multiply it by a second fraction that will convert the time units from hours to seconds.
Let’s first consider the units of distance and recall that one mile is approximately equal to 1.6 kilometers and then that one kilometer is equal to 1000 meters. Therefore, one mile is equal to 1.6 times 1000 or 1600 meters. Let’s now return to this first fraction. We needed to have a numerator in units of meters and a denominator in units of miles so that these miles cancel leaving us with distance units of meters. And we need it to equal one so that it doesn’t change the value. So we can use one mile and 1600 meters.
Let’s now consider the second fraction and how to convert our units of time. Recall that one hour is equal to 3600 seconds. And that’s because one hour is equal to 60 minutes and one minute is equal to 60 seconds. In this fraction, we need the numerator to have units of hours so that the units cancel with our original hours and the denominator needs to have units of seconds. So we can use values of one hour and 3600 seconds. So the value of one mile per hour in meters per second is one times 1600 over one times one over 3600 which is equal to 0.4 recurring meters per second. Now the question asks for this to two decimal places, so this becomes 0.44 meters per second.
So the answer is one mile per hour is equal to 0.44 meters per second to two decimal places.
