Question

How do you convert \[36{\rm{cm}}/{\rm{sec}}\] to mph?

Answer 1

Hint:
Here, we will first convert 1 cm to 1 mile and then we will convert 1 sec into an hour by using the basic conversion of length and time. Then we will divide the value of 1 mile by 1 hour to get the value of 1 mph. We will then multiply the resulting value by 36 to find the required value.

Formula used:
\[1\] km \[ \approx 0.62\] miles

Complete step by step solution:
We are given \[36{\rm{cm/sec}}\] and we have to convert this to mph, which stands for “miles per hour”.
For this, let us first calculate the value of \[1{\rm{cm/sec}}\] in terms of mph.
 We will convert 1 cm into miles.
We know that \[1{\rm{km}} = 1000{\rm{m}}\] and, \[1{\rm{m}} = 100{\rm{cm}}\]. Using these conversions, we will convert km to cm as
\[1{\rm{km}} = 1000 \times 100 = 100000{\rm{cm}}\] ……….\[(1)\]
Using the conversion \[1\] km \[ \approx 0.62\] miles in equation \[(1)\], we get
\[ \Rightarrow 0.62\] miles \[ = 100000{\rm{cm}}\]…………\[(2)\]
To find the equivalent of \[1\] cm in terms of miles, we will divide both sides of equation \[(2)\] by \[100000\]. Thus, we get
\[ \Rightarrow \dfrac{{0.62}}{{100000}}\] miles \[ = \dfrac{{100000}}{{100000}}\] cm
\[ \Rightarrow 1{\rm{cm}} = 0.0000062\] miles ……….\[(3)\]
Now, we have to convert \[1\] second into an hour. We know that \[1\] hour \[ = 60\] minutes and \[1\] minute \[ = 60\] seconds. Using these conversions, we can convert hour to seconds as
\[1\] hour\[ = 60 \times 60 = 3600\] seconds ……….\[(4)\]
To convert \[1\] second into an hour, let us divide both sides of equation \[(4)\] by \[3600\]. Thus, we get
\[\dfrac{1}{{3600}}\] hour \[ = \dfrac{{3600}}{{3600}}\] seconds
\[ \Rightarrow 1\] second \[ = \dfrac{1}{{3600}}\] hours .......... \[(5)\]
Therefore, to convert \[1{\rm{cm}}/{\rm{sec}}\] into mph, we will divide equation \[(3)\] by equation \[(5)\]. Hence,
\[1{\rm{cm}}/{\rm{sec}} = \dfrac{{0.0000062}}{{\left( {\dfrac{1}{{3600}}} \right)}}\] mph
Taking the denominator’s denominator to the numerator on the RHS, we get
\[ \Rightarrow 1{\rm{cm}}/{\rm{sec}} = 0.0000062 \times 3600 = 0.02232\] mph ……….\[(6)\]
Now, to convert \[36{\rm{cm}}/{\rm{sec}}\] to mph, we will multiply both sides of equation \[(6)\] by 36. Therefore,

\[36{\rm{cm}}/{\rm{sec}} = 36 \times 0.02232 = 0.80352\] mph


Note:
To solve such problems, we can use basic conversions to find the value in the required units. We should keep in mind that we have to first find the equivalent of one unit and multiply the conversion quantity by the required value. We know that meter, centimetre, kilometre, and miles are units of length or distance. In addition, second, minute and hour are the units of time.