Video: Converting Common Units of Speed

The speed limit on some interstate highways is roughly 100 km/h. What is this in meters per second? How many miles per hour is this? Note: 1 mile = 1.6 km

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Video Transcript

The speed limit on some interstate highways is roughly 100 kilometers per hour. What is this in meters per second? How many miles per hour is this? Note, one mile equals 1.6 kilometers.

First, we’ll solve for this speed written not in kilometers per hour as it’s given but in meters per second. To do that, we’ll first write out our given speed as a fraction. Currently, this fraction has distance units of kilometers and time units of hours. And we want to change those to meters and seconds, respectively. When we recall or look up the unit conversions for those distances and times, we find that one kilometer is equal to 1000 meters and one hour is equal to 3600 seconds. Now, what we’ll do is we’ll take these two conversion factors and apply them to our given information.

First, we’ll multiply our 100 kilometers per hour by a conversion factor from kilometers to meters. Notice that if we perform this multiplication, our units of kilometers cancel out. Next, we multiply by our unit conversion from hours to seconds. Notice again that our units of hours, our unwanted time unit, cancel out. And we’re left in this fraction with units of meters and seconds just as we wanted. When we multiply these three fractions together, we find a result of 27.8 meters per second. That’s a speed of 100 kilometers per hour converted to units of meters per second.

Next, we move on to expressing our initially given speed in kilometers per hour to a speed in miles per hour. And we’re told that one mile is equal to 1.6 kilometers. Once again, we write out our given speed as a fraction. And using the conversion factor we’re given in the problem statement, multiply it by it, so that we can see that units of kilometers cancel as distance. And we’re left with distance units of miles divided by time units of hours. When we multiply these two fractions together, we find a result of 62.5 miles per hour. That’s the speed limit expressed in those units.

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