Question

Convert $45km/hr$ to $m/\sec $.
A.$10$
B.$10\dfrac{1}{2}$
C.$90$
D.$12\dfrac{1}{2}$

Answer 1

Hint: We know that kilometer and meter are the units of length and hour and second are units of time. But why do we need different units for the same quantity? The answer is simple, for Longer distances, the bigger unit is better suited and for shorter distances, smaller unit is suited. All we need to know is the conversion from one unit to the other.

Complete step-by-step answer:
Length is one of the most widely used fundamental quantities. The SI unit of length is meters. Meter is defined as the path travelled by light in vacuum during a time interval of ${{\left( \dfrac{1}{299792458} \right)}^{th}}$ part of a seconds. Kilometer is a much bigger quantity to measure length. There are units to measure the length, for example: miles, foot, inch, etc.
Time is another most widely used fundamental quantity. The SI unit of time is seconds. Second is defined as ${{\left( \dfrac{1}{86400} \right)}^{th}}$ part of a day.
Over here, we need to convert kilometers per hour into meters per second.
The conversion scale is the most important factor to answer this question.
For this conversion, we need a scale to convert kilometer to meter and hours to second. So, by the definition of kilo:
$kilo=1000$ .
Hence, $1km=1000m$ . - (1)
And by the definition of hours:
$1hour=3600seconds$
Therefore, $1km/h=\dfrac{1000}{3600}m/\sec $
$\Rightarrow 1km/h=\dfrac{5}{18}m/\sec $ - (2)
Multiplying equation (2) by $45$ , we get:
$45\left( 1km/h=\dfrac{5}{18}m/\sec \right)$
$\Rightarrow 45km/h=45\times \dfrac{5}{18}m/\sec $
$\Rightarrow 45km/h=\dfrac{25}{2}m/\sec =12\dfrac{1}{2}m/\sec $
Hence, option D. $12\dfrac{1}{2}$ , is the correct option.

Note: We must always remember the correct conversion scale in the conversion from one unit to the other. We must be very careful in writing the conversion scale, and not to confuse conversion scale with some other scale. Different units are used to measure different amounts of quantities. For length, two very different units are Kilometers and Miles. We can only compare or convert things of the same quantities.