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.
