Question

How do you convert 32.4 meters per second to miles per hour? \[\]

Answer 1

Hint: We find many number hours are there in 1 second and how many miles are there in 1 metre. We convert the given measurement of speed 32.4 meters per second by multiplying ratio number miles in meter to number of seconds in an hour.\[\]

Complete answer:
We know that speed is distance covered per unit times. We measure distance in meters. Kilometres (km) , miles etc. We measure time second, minutes, hour etc. Then unit of the speed becomes metre per second (m/s) , kilometre per hour (km/h) and miles per hour (mph).\[\]
Let us convert 1 m/s to 1 miles/hour first. We know that 1 miles is approximately 1.61 km. We also know 1 km is 1000m. So we have;
\[1\text{ miles}=1.60\times 1000=1600\text{ m}\]
 So the number of miles in 1 m is
\[1\text{ m}=\dfrac{1}{1600}\text{ miles}\]
We know that 1 hour is 60 minutes and 1 minute is 60 second. So the number of seconds in one hour is $60\times 60=3600$. So the number of hours in 1 second is
\[1\text{ s}=\dfrac{1}{3600}\text{ hr}\]
No we can convert 1 m/s to miles per hour as
\[1\text{ m/s}=\dfrac{1\text{ m}}{1\text{ s}}=\dfrac{\dfrac{1}{1600}\text{ miles}}{\dfrac{1}{3600}\text{ hour}}=\dfrac{1}{1600}\times \dfrac{3600}{1}=\dfrac{36}{16}=\dfrac{9}{4}\text{ mph}\]
We multiply $\dfrac{9}{4}$ with 32.4 to convert 324m/s into miles per hour as
\[32.4\text{ m/s}=32.4\times \dfrac{9}{4}=8.1\times 9=72.9\text{ mph}\]

Note: We can use $1\text{ miles}=1.60934\text{ km}$ to calculate more accurately. We can convert back from miles per hour to m/ sec by multiplying $\dfrac{4}{9}$ . We can convert m/s to km/hr by multiplying $\dfrac{18}{5}$ and convert back to m/s by multiplying $\dfrac{5}{18}$. We note that m/s SI units of speed and miles per hour are the imperial unit of speed.