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Question: Convert the acceleration \(10m{s^{ - 2}}\) into \(km{h^{ - 2}}\)...

Convert the acceleration 10ms−210m{s^{ - 2}} into kmh−2km{h^{ - 2}}

Explanation

Solution

As, we know that 1km=1000m1km = 1000m, then 1m=11000km1m = \dfrac{1}{{1000}}km and we also know that 1h=60min⁡=60×60sec⁡=3600sec⁡1h = 60\min = 60 \times 60\sec = 3600\sec , then 1sec⁡=13600h1\sec = \dfrac{1}{{3600}}h, on substituting the values we will get the required result.

Complete step-by-step answer:
We, have to convert the acceleration 10ms−210m{s^{ - 2}} into kmh−2km{h^{ - 2}}
For this, we know that
1km=1000m1km = 1000m
And 1h=60min⁡=60×60sec⁡=3600sec⁡1h = 60\min = 60 \times 60\sec = 3600\sec
But as we have to convert the mm into kmkm so we can write it as, 1m=11000km1m = \dfrac{1}{{1000}}km
And seconds into hours so we can write, 1sec⁡=13600h1\sec = \dfrac{1}{{3600}}h
Now, as acceleration is a=10ms−2a = 10m{s^{ - 2}}
Now convert meter into kilometer and seconds into hours by using the above relations, we get
⇒a=10ms2\Rightarrow a = 10\dfrac{m}{{{s^2}}}
⇒a=10×11000(13600)2\Rightarrow a = \dfrac{{10 \times \dfrac{1}{{1000}}}}{{{{\left( {\dfrac{1}{{3600}}} \right)}^2}}}
⇒a=10×(3600)21000\Rightarrow a = \dfrac{{10 \times {{\left( {3600} \right)}^2}}}{{1000}}
⇒a=36000×36\Rightarrow a = 36000 \times 36
⇒a=1296000\Rightarrow a = 1296000
⇒a=1.296×106kmh−2\Rightarrow a = 1.296 \times {10^6}km{h^{ - 2}}
This is the required acceleration in kmh−2km{h^{ - 2}}

Additional information:
Definition of kilometer: a kilometer is a decimal multiple of the meter, the international unit of the length, approximately equal to 39370.07 inches. A kilometer is now used officially for expressing distance between two places or points.
Definition of meter: A meter is the base unit of the length in the international system of units. Therefore, 1km=1000 meters.
Definition of hours: A period of time equal to 60 minutes that is 3600 seconds.
Definition of seconds: it is measured as the smallest unit of time. Therefore, 1sec⁡=13600h1\sec = \dfrac{1}{{3600}}h

Note: for this problem, there is a standard equation for this type of conversion. To convert a kilometer per hour into meters per second, we need to multiply by 5 and divide by 18. This standard form got from this 1km10001h23600×3600\dfrac{{\dfrac{{1km}}{{1000}}}}{{\dfrac{{1{h^2}}}{{3600 \times 3600}}}} fraction which we used in the solution to solve. When we solve this fraction, we will get above term.