Answer :
Certainly! Here’s a detailed step-by-step solution for each part of the question:
### 8. Express the following speeds in meters per second:
To convert from kilometers per hour (km/h) to meters per second (m/s), we use the conversion factor:
[tex]\[ 1 \, \text{km/h} = \frac{1000 \, \text{meters}}{3600 \, \text{seconds}} = \frac{5}{18} \, \text{m/s} \][/tex]
(a) 36 km per hour:
[tex]\[ 36 \times \frac{5}{18} = 10 \, \text{m/s} \][/tex]
(b) 60 km per hour:
[tex]\[ 60 \times \frac{5}{18} = 16.67 \, \text{m/s} \][/tex]
(c) 126 km per hour:
[tex]\[ 126 \times \frac{5}{18} = 35 \, \text{m/s} \][/tex]
### 9. Express the following speeds in meters per minute:
To convert from kilometers per hour (km/h) to meters per minute (m/min), we use the conversion factor:
[tex]\[ 1 \, \text{km/h} = \frac{1000 \, \text{meters}}{60 \, \text{minutes}} = \frac{1000}{60} \, \text{m/min} \][/tex]
(a) 54 km per hour:
[tex]\[ 54 \times \frac{1000}{60} = 900 \, \text{m/min} \][/tex]
(b) 63 km per hour:
[tex]\[ 63 \times \frac{1000}{60} = 1050 \, \text{m/min} \][/tex]
(c) 132 km per hour:
[tex]\[ 132 \times \frac{1000}{60} = 2200 \, \text{m/min} \][/tex]
### 10. Express the following speeds in km per hour:
To convert from meters per second (m/s) to kilometers per hour (km/h), we use the conversion factor:
[tex]\[ 1 \, \text{m/s} = \frac{3600 \, \text{seconds}}{1000 \, \text{meters}} = \frac{18}{5} \, \text{km/h} \][/tex]
(a) 35 m per second:
[tex]\[ 35 \times \frac{18}{5} = 126 \, \text{km/h} \][/tex]
(b) 45 m per second:
[tex]\[ 45 \times \frac{18}{5} = 162 \, \text{km/h} \][/tex]
For part (c), we need to convert from meters per minute (m/min) to kilometers per hour:
[tex]\[ 1 \, \text{m/min} = \frac{60 \, \text{minutes}}{1000 \, \text{meters}} = \frac{3.6}{1} \, \text{km/h} \][/tex]
(c) 900 m per minute:
[tex]\[ 900 \times \frac{3.6}{1} = 54 \, \text{km/h} \][/tex]
### 11. A man can cover [tex]\( 17 \frac{1}{2} \, \text{km} \)[/tex] in 5 hours. Find his speed in:
First, we convert the distance from kilometers to meters:
[tex]\[ 17.5 \, \text{km} = 17500 \, \text{m} \][/tex]
(a) Meters per minute:
Convert hours to minutes:
[tex]\[ 5 \, \text{hours} = 5 \times 60 = 300 \, \text{minutes} \][/tex]
[tex]\[ \text{Speed} = \frac{17500 \, \text{m}}{300 \, \text{min}} = 58.33 \, \text{m/min} \][/tex]
(b) Meters per second:
Convert hours to seconds:
[tex]\[ 5 \, \text{hours} = 5 \times 3600 = 18000 \, \text{seconds} \][/tex]
[tex]\[ \text{Speed} = \frac{17500 \, \text{m}}{18000 \, \text{s}} \approx 0.972 \, \text{m/s} \][/tex]
I hope that helps! If you have any more questions, feel free to ask.
### 8. Express the following speeds in meters per second:
To convert from kilometers per hour (km/h) to meters per second (m/s), we use the conversion factor:
[tex]\[ 1 \, \text{km/h} = \frac{1000 \, \text{meters}}{3600 \, \text{seconds}} = \frac{5}{18} \, \text{m/s} \][/tex]
(a) 36 km per hour:
[tex]\[ 36 \times \frac{5}{18} = 10 \, \text{m/s} \][/tex]
(b) 60 km per hour:
[tex]\[ 60 \times \frac{5}{18} = 16.67 \, \text{m/s} \][/tex]
(c) 126 km per hour:
[tex]\[ 126 \times \frac{5}{18} = 35 \, \text{m/s} \][/tex]
### 9. Express the following speeds in meters per minute:
To convert from kilometers per hour (km/h) to meters per minute (m/min), we use the conversion factor:
[tex]\[ 1 \, \text{km/h} = \frac{1000 \, \text{meters}}{60 \, \text{minutes}} = \frac{1000}{60} \, \text{m/min} \][/tex]
(a) 54 km per hour:
[tex]\[ 54 \times \frac{1000}{60} = 900 \, \text{m/min} \][/tex]
(b) 63 km per hour:
[tex]\[ 63 \times \frac{1000}{60} = 1050 \, \text{m/min} \][/tex]
(c) 132 km per hour:
[tex]\[ 132 \times \frac{1000}{60} = 2200 \, \text{m/min} \][/tex]
### 10. Express the following speeds in km per hour:
To convert from meters per second (m/s) to kilometers per hour (km/h), we use the conversion factor:
[tex]\[ 1 \, \text{m/s} = \frac{3600 \, \text{seconds}}{1000 \, \text{meters}} = \frac{18}{5} \, \text{km/h} \][/tex]
(a) 35 m per second:
[tex]\[ 35 \times \frac{18}{5} = 126 \, \text{km/h} \][/tex]
(b) 45 m per second:
[tex]\[ 45 \times \frac{18}{5} = 162 \, \text{km/h} \][/tex]
For part (c), we need to convert from meters per minute (m/min) to kilometers per hour:
[tex]\[ 1 \, \text{m/min} = \frac{60 \, \text{minutes}}{1000 \, \text{meters}} = \frac{3.6}{1} \, \text{km/h} \][/tex]
(c) 900 m per minute:
[tex]\[ 900 \times \frac{3.6}{1} = 54 \, \text{km/h} \][/tex]
### 11. A man can cover [tex]\( 17 \frac{1}{2} \, \text{km} \)[/tex] in 5 hours. Find his speed in:
First, we convert the distance from kilometers to meters:
[tex]\[ 17.5 \, \text{km} = 17500 \, \text{m} \][/tex]
(a) Meters per minute:
Convert hours to minutes:
[tex]\[ 5 \, \text{hours} = 5 \times 60 = 300 \, \text{minutes} \][/tex]
[tex]\[ \text{Speed} = \frac{17500 \, \text{m}}{300 \, \text{min}} = 58.33 \, \text{m/min} \][/tex]
(b) Meters per second:
Convert hours to seconds:
[tex]\[ 5 \, \text{hours} = 5 \times 3600 = 18000 \, \text{seconds} \][/tex]
[tex]\[ \text{Speed} = \frac{17500 \, \text{m}}{18000 \, \text{s}} \approx 0.972 \, \text{m/s} \][/tex]
I hope that helps! If you have any more questions, feel free to ask.
