Express each of the following in m s ^-1:

(a) 10 km h^-1

(b) 18 km min^-1

(a) As,

$10 \text{ km h}^{-1} = \dfrac{10 \text{ km}}{1\text{h}} = \dfrac {10 \times 1000 \text{m}}{60 \times 60 \text{s}} \\[1em] \Rightarrow 10 \text{ km h}^{-1} = \dfrac {10 \times 10 \text{m}}{6 \times 6 \text{s}} \\[1em] \Rightarrow 10 \text{ km h}^{-1} = 2.78 \space \dfrac{\text{m}}{\text{s}}$

Hence, 10 km h^-1 is equal to 2.78 ms^-1.

(b) As,

$18 \text{ km min}^{-1} = \dfrac{18 \text{ km}}{1 \text{ min}} = \dfrac {18 \times 1000 \text{m}}{60 \text{s}} \\[1em] \Rightarrow 18 \text{ kmh}^{-1} = \dfrac {18 \times 100 \text{ m}}{6 \text{s}} \\[1em] \Rightarrow 18 \text{ kmh}^{-1}= 300 \space \dfrac{\text{ m}}{\text{s}}$

Hence, 18 km h^-1 is equal to 300 m s^-1.