EXERCISE 6.4
Question 1
$1 \mathrm{~km} / \mathrm{h}=\frac{5}{18} \mathrm{~m} / \mathrm{sec}$
i) $72 \mathrm{~km} / \mathrm{h}=72 \times \frac{5}{18}=4 \times 5=20 \mathrm{~m} / \mathrm{sec}$
ii) $9 \mathrm{~km} / \mathrm{h}=9 \times \frac{5}{18}=\frac{5}{2} \mathrm{~m} / \mathrm{sec}=2.5 \mathrm{~m} / \mathrm{sec}$
iii) $1.2 \mathrm{~km}= / \mathrm{min}, 1.2 \times \frac{1000 \mathrm{~m}}{60 \mathrm{sec}}=\frac{1200 \mathrm{~m} / \mathrm{sec}}{60}=20 \mathrm{~m} / \mathrm{sec}$
iv) $600 \mathrm{~m} / \mathrm{hour}$ = $600 \times \frac{1 \mathrm{~m}}{60\times60 \mathrm{sec}}$ = $\frac{1}{6} \mathrm{~m} / \mathrm{sec}$
Question 2
$1 \mathrm{~m} / \mathrm{sec}=\frac{18}{5} \mathrm{~km} / \mathrm{h}$
i) $15 \mathrm{~m} / \mathrm{sec}=1 \mathrm{5} \times \frac{18}{5} \mathrm{km} / \mathrm{h}=54 \mathrm{~km} / \mathrm{h}$
ii) $5 \mathrm{~m} / \mathrm{sec}$ =$\frac{1{5}}{10} \times \frac{18}{5}$= $\frac{54}{10} \mathrm{~km} / \mathrm{h}=5.4 \mathrm{~km} / \mathrm{h} .$
Question 3
$\begin{aligned} 30 \mathrm{~m} / \mathrm{sec}=30 \times \frac{18}{8} \mathrm{~km} / \mathrm{h} &=108 \mathrm{~km} / \mathrm{h} . \\ \text { since, } 108 \mathrm{~km} / \mathrm{h} &>30 \mathrm{~km} / \mathrm{h} \\ \text { So, } 30 \mathrm{~m} / \mathrm{sec} &>30 \mathrm{~km} / \mathrm{L} \end{aligned}$
Question 4
i) Given speed of aeroplane = 72km\h
Also distance between two cities = 1800km
We know time= $\frac{\text { Distance }}{\text { Speed }}$
$=\frac{1800}{720}$ hour
$=\frac{5}{2}$ honss
Time $=2 \frac{1}{2}$ hour
ii) Here time = 40 min, speed = 720km\h
$\frac{720 \times 1000}km{60 \mathrm{~min}} \mathrm{~m}$
Now Distance $=$ Speed $\times$ Time
$=12,000 \times 40 \mathrm{~m}$
$=480000 \mathrm{~m}$
$=\frac{480000}{1000} \mathrm{~km}$
Distance $=480 \mathrm{~km}$
iii) Given Time $=15 \mathrm{sec}$, Speed $=720 \mathrm{~km} / \mathrm{h}$
$=720 \times \frac{5}{18} \mathrm{~m} / \mathrm{sec}$
$=200 \mathrm{~m} / \mathrm{sec}$
Distance =speed $\times$ Time
$=15 \times 200 \mathrm{~m}$
$\begin{aligned} &=3000 \mathrm{~m} \\ &=\frac{3000}{1000} \mathrm{~km} \\ \therefore \quad \text { Distance } &=3 \mathrm{~km} \end{aligned}$
Question 5
Given speed = 6km\h
$=\frac{6 \times 1000 \mathrm{~m}}{60 \mathrm{~min}}$
$=100 \mathrm{~m} / \mathrm{min}$
i) Distance
$\begin{aligned} &=\text { Speed } \times \text { Time } \\ &=100 \times 5 \\ &=500 \text { metres } \\ &=0.5 \mathrm{~km} \end{aligned}$
ii)
$\begin{aligned} \text { Time }=\frac{\text { Distance }}{\text { speed }} &=\frac{200}{100} \\ \text { Time } &=2 \mathrm{~min} \end{aligned}$
Question 6
Given Distance
$\begin{aligned} &=50 \text { metres } \\ &=\frac{50}{1000} \mathrm{~km} \\ &=0.05 \mathrm{~km} \\ &=\frac{1}{20} \mathrm{~km} \end{aligned}$
Total Distance $=2 \times \frac{1}{20} \mathrm{~km}=\frac{1}{10} \mathrm{~km}$
Time taken
$\begin{aligned} &=5 \mathrm{~min} \\ &=\frac{5}{60} \text { hours } \end{aligned}$
Now, speed $=\frac{\text { Distance }}{\text { Time }}$
$=\frac{(1 / 10) \mathrm{km}}{(5 / 60) \mathrm{hour}}$
$=\frac{1}{10} \times \frac{60}{5}$
$=\frac{6}{5}$
Speed $=1.2 \mathrm{~km} / \mathrm{k}$
Question 7
Given Time $=48$ minutes $=\frac{48}{60}$ hours
$=\frac{4}{5}$ hours.
Speed $=50 \mathrm{~km} / \mathrm{h}$
$\begin{aligned} \text { Distance } &=\text { Speed } \times \text { Jime } \\ &=50 \times \frac{4}{5} \\ &=40 \mathrm{~km} . \end{aligned}$
$\begin{aligned} \text { Time }=? & \text { : Speed }=30 \mathrm{~km} / \mathrm{k} \\ \text { Time }=& \frac{\text { Distance }}{\text { speed }} \end{aligned}$
$=\frac{4}{3}$ hours
$=\frac{4}{3} \times 60$ min
∴ Time $=80 \mathrm{~min}$
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