Question

Change the speed of $6m/s$ into $km/h$.

Answer 1

In order to solve these types of problems, we have to use the conversion of metre into kilometre and second into hour.

Complete step by step solution:
We know that metre and kilometre are the units of distance & displacement and the conversion of them is given as
$1km = 1000m = {10^3}m$
So, $1m = \dfrac{1}{{1000}}km = \dfrac{1}{{{{10}^3}}}km$
$1m = {10^{ - 3}}km$ …..(1)
We also know that second minute & hour are the units of time and the conversion of them is given as
$1hour = 60minute$ …..(2)
& $1minute = 60seconds$
So, $60minute = 60 \times 60seconds$
$= 3600seconds$ ..…(3)
Hence, from equation (2) & (3)
$1hour = 3600seconds$
So, $1second = \dfrac{1}{{3600}}hour$ ….(4)
Now, we have to convert into $6m/s$ into $km/h$
So, $6m/s = 6 \times \left( {\dfrac{{1m}}{{1\sec }}} \right)$
From equation (1) & (4)
$6m/s = 6 \times \left( {\dfrac{{{{10}^{ - 3}}km}}{{\dfrac{1}{{3600}}hr}}} \right)$
$= 6 \times {10^{ - 3}} \times 3600km/hr$
$= \dfrac{{6 \times 3600}}{{{{10}^3}}}km/hr$
$= \dfrac{{6 \times 3600}}{{1000}} = \dfrac{{6 \times 36}}{{10}}$
$= \dfrac{{216}}{{10}}km/hr$
$6m/s = 21.6km/hr$

Note: In order to solve conversion problems, we have to use the basic conversion relation i.e.,
$1km = 1000m$
$1m = 100cm$
$1m = 60\sec$1
$1hr = 60\min$
$1mm = {10^{ - 3}}m$
$1\mu m = {10^{ - 6}}m$