Arrange the following speeds in increasing order — 10 m s^-1, 1 km min^-1, 18 km h^-1.

In order to arrange in increasing order of speeds, the units of the given speeds must be same.

Hence, we convert all the three in m s^-1.

(a) 10 m s^-1 = 10 m s^-1   …. [1]
(already in m s^-1)

(b) 1 km min^-1,

$\text{1 km min}^{-1} = \dfrac{\text{1 km}}{\text{1 min}} = \dfrac {1 \times 1000 \text{m}}{ 60 \text{s}} \\[0.5em] \Rightarrow \text{1 km min}^{-1} = \dfrac {1 \times 100 \text{m}}{6\text{s}} \\[0.5em] \Rightarrow \text{1 km min}^{-1} = \dfrac {16.66 \times \text{m}}{\text{s}} \\[0.5em]$

Hence,
1 km min^-1 = 16.66 m s^-1   …. [2]

(c) 18 km h^-1,

As,

$\text{18 km h}^{-1} = 18 \dfrac{km}{h} = \dfrac {18 \times 1000 m}{60 \times 60 s} \\[0.5em] \Rightarrow \text{18 km h}^{-1} = \dfrac {18 \times 10 m}{6 \times 6s} \\[0.5em] \Rightarrow \text{18 km h}^{-1} = \dfrac {5 \times m}{s} \\[0.5em]$

Hence,
18km h^-1 = 5 m s^-1   …. [3]

From 1, 2 and 3, we get the increasing order as follows —

18 km h^-1, 10 m s^-1, 1 km min^-1.