Video Transcript
Which of the following is
false? (a) 72 kilometers per hour equals
20 meters per second. (b) Three kilometers per minute
equals 50 centimeters per second. (c) 15 meters per second equals 54
kilometers per hour. Or (d) 42 meters per minute equals
70 centimeters per second.
To verify each equation, we need to
convert the units on one side of the equation into the units on the other side of
the equation. Let’s convert the units from the
left-hand side of each equation into the units on the right-hand side of each
equation and then compare the coefficients to see if they are true or false.
So, starting with (a), we need to
convert kilometers into meters and hours into seconds. One kilometer is equal to 1000
meters, and one hour is equal to 3600 seconds. We therefore have 72 kilometers per
hour equals 72 times 1000 meters per 3600 seconds. It can be helpful to write these as
fractions so we can see the multiplication and division more clearly. So we have 72000 meters divided by
3600 seconds. Simplifying this, we obtain 20
meters divided by one second, or 20 meters per second. Therefore, equation (a) is
true.
Next, for equation (b), we need to
convert kilometers into centimeters and minutes into seconds. One kilometer equals 1000
meters. So in centimeters, one kilometer is
100000 centimeters, or 10 to the five centimeters. And similarly, one minute equals 60
seconds. Therefore, we have three kilometers
per minute equals three times 10 to the five centimeters per 60 seconds. Simplifying this fraction, we get
three kilometers per minute equals 5000 centimeters per second. Therefore, the false equation is
(b) three kilometers per minute equals 50 centimeters per second.
