Express each of the following in m s -1 —
(a) 1 km h-1
(b) 18 km min-1
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(a) As,
1km h−1=1km1h=1×1000m60×60s⇒1km h−1=1×10m6×6s⇒1km h−1=0.278ms1 \text{km h}^{-1} = \dfrac{1 \text{km}}{1\text{h}} = \dfrac {1 \times 1000 \text{m}}{60 \times 60 \text{s}} \\[1em] \Rightarrow 1 \text{km h}^{-1} = \dfrac {1 \times 10 \text{m}}{6 \times 6 \text{s}} \\[1em] \Rightarrow 1 \text{km h}^{-1} = 0.278\dfrac {\text{m}}{\text{s}}1km h−1=1h1km=60×60s1×1000m⇒1km h−1=6×6s1×10m⇒1km h−1=0.278sm
Hence, 1 km h-1 is equal to 0.278 ms-1.
(b) As,
18km min−1=18kmmin=18×1000m60s⇒18kmh−1=18×100m6s⇒18kmh−1=300 ms18 \text{km min}^{-1} = 18 \dfrac{\text{km}}{\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 \dfrac{\text{ m}}{\text{s}}18km min−1=18minkm=60s18×1000m⇒18kmh−1=6s18×100m⇒18kmh−1=300s m
Hence, 18 km h-1 is equal to 300 m s-1.
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