Answer :
To solve these questions, we need to use the basic formulas involved in motion, specifically the relationship between speed, distance, and time.
The formula to find the speed is:
[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]
And to find the distance, the formula is:
[tex]\text{Distance} = \text{Speed} \times \text{Time}[/tex]
Let's solve these questions step-by-step:
3. Find the speeds:
a) A distance of 600 km in 8 hours:
[tex]\text{Speed} = \frac{600 \text{ km}}{8 \text{ hours}} = 75 \text{ km/h}[/tex]
b) A distance of 31.64 km in 7 hours:
[tex]\text{Speed} = \frac{31.64 \text{ km}}{7 \text{ hours}} \approx 4.52 \text{ km/h}[/tex]
c) A distance of 136.8 m in 18 seconds:
[tex]\text{Speed} = \frac{136.8 \text{ m}}{18 \text{ seconds}} = 7.6 \text{ m/s}[/tex]
d) A distance of [tex]4 \times 10^4[/tex] m in [tex]10^{-2}[/tex] seconds:
[tex]\text{Speed} = \frac{4 \times 10^4 \text{ m}}{10^{-2} \text{ seconds}} = 4 \times 10^6 \text{ m/s}[/tex]
e) A distance of [tex]5 \times 10^5[/tex] cm in [tex]2 \times 10^{-3}[/tex] seconds:
First, convert the distance to meters: [tex]5 \times 10^5 \text{ cm} = 5 \times 10^3 \text{ m}[/tex]
[tex]\text{Speed} = \frac{5 \times 10^3 \text{ m}}{2 \times 10^{-3} \text{ seconds}} = 2.5 \times 10^6 \text{ m/s}[/tex]
f) A distance of [tex]10^8[/tex] mm in 30 minutes (in km/h):
First, convert the distance to kilometers and time to hours:
[tex]10^8 \text{ mm} = 10^5 \text{ m} = 100 \text{ km}[/tex]
30 minutes = 0.5 hours
[tex]\text{Speed} = \frac{100 \text{ km}}{0.5 \text{ hours}} = 200 \text{ km/h}[/tex]
g) A distance of 500 m in 10 minutes (in km/h):
First, convert the distance to kilometers and time to hours:
500 m = 0.5 km
10 minutes = [tex]\frac{10}{60}[/tex] hours = [tex]\frac{1}{6}[/tex] hours
[tex]\text{Speed} = \frac{0.5 \text{ km}}{\frac{1}{6} \text{ hours}} = 3 \text{ km/h}[/tex]
4. Find the distance traveled:
a) At a speed of 55 km/h for 2 hours:
[tex]\text{Distance} = 55 \text{ km/h} \times 2 \text{ hours} = 110 \text{ km}[/tex]
Convert to meters:
[tex]110 \text{ km} = 110,000 \text{ m}[/tex]
b) At a speed of 40 km/h for 1/4 hour:
[tex]\text{Distance} = 40 \text{ km/h} \times \frac{1}{4} \text{ hour} = 10 \text{ km}[/tex]
Convert to meters:
[tex]10 \text{ km} = 10,000 \text{ m}[/tex]
c) At a speed of 338.4 km/h for 10 minutes:
First, convert time to hours:
10 minutes = [tex]\frac{10}{60}[/tex] hours = [tex]\frac{1}{6}[/tex] hour
[tex]\text{Distance} = 338.4 \text{ km/h} \times \frac{1}{6} \text{ hour} \approx 56.4 \text{ km}[/tex]
Convert to meters:
[tex]56.4 \text{ km} = 56,400 \text{ m}[/tex]
d) At a speed of 15 m/s for 5 minutes:
First, convert time to seconds:
5 minutes = 300 seconds
[tex]\text{Distance} = 15 \text{ m/s} \times 300 \text{ seconds} = 4,500 \text{ m}[/tex]
e) At a speed of 14 m/s for 1 hour:
First, convert time to seconds:
1 hour = 3600 seconds
[tex]\text{Distance} = 14 \text{ m/s} \times 3600 \text{ seconds} = 50,400 \text{ m}[/tex]
f) At a speed of [tex]4 \times 10^3[/tex] m/s for [tex]2 \times 10^{-2}[/tex] seconds:
[tex]\text{Distance} = 4 \times 10^3 \text{ m/s} \times 2 \times 10^{-2} \text{ s} = 80 \text{ m}[/tex]
g) At a speed of [tex]8 \times 10^5[/tex] cm/s for 2 minutes:
First, convert speed to meters per second and time to seconds:
[tex]8 \times 10^5 \text{ cm/s} = 8 \times 10^3 \text{ m/s}[/tex]
2 minutes = 120 seconds
[tex]\text{Distance} = 8 \times 10^3 \text{ m/s} \times 120 \text{ seconds} = 960,000 \text{ m}[/tex]
