Convert $54 k m h^{- 1}$ into $m s^{- 1}$

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Solution

Let $v = 54 k m h^{- 1} = n_{2} m s^{- 1}$
Dimensions of the velocity are $[v] = L T^{- 1}, a = 0, b = 1, c = - 1$
Now, using the conversion factor:

$n_{2} = 54 {[\frac{k g}{g}]}^{0} {[\frac{k m}{m}]}^{1} {[\frac{h}{s}]}^{- 1}$

$= 54 \times 1 \times 1000 \times [3600]^{- 1}$

$= \frac{54 \times 1000}{3600} = 15$

Hence, $54 k m h^{- 1} = 15 m s^{- 1}$

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