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Answer :
- Calculate velocity by dividing distance by time: $v = \frac{d}{t}$.
- Convert m/s to km/h by multiplying by 3.6.
- Convert km/h to m/s by dividing by 3.6.
- Apply the formulas to find the unknown values: $\boxed{v, d, t}$.
### Explanation
1. Understanding the Problem
The problem involves calculating velocities, distances, and times using the formula $velocity = \frac{distance}{time}$. We also need to perform unit conversions between meters, kilometers, seconds, and hours.
2. Question 1
1. A motorist travelled 900 m in 45 seconds.
a) To find the velocity in m/s, we divide the distance by the time: $v = \frac{900 \text{ m}}{45 \text{ s}} = 20 \text{ m/s}$.
b) To convert this to km/h, we multiply by 3.6: $20 \text{ m/s} \times 3.6 = 72 \text{ km/h}$.
3. Question 2
2. An athlete completed a 100 m race in 10 seconds. The velocity is $v = \frac{100 \text{ m}}{10 \text{ s}} = 10 \text{ m/s}$.
4. Question 3
3. A rocket travelled 20 km in 8 seconds. The velocity is $v = \frac{20 \text{ km}}{8 \text{ s}} = 2.5 \text{ km/s}$. To convert to km/h, we multiply by 3600: $2.5 \text{ km/s} \times 3600 = 9000 \text{ km/h}$.
5. Question 4
4. An airplane flew 430 km in 55 minutes. First, convert 55 minutes to hours: $t = \frac{55}{60} \text{ h}$. Then, the velocity is $v = \frac{430 \text{ km}}{\frac{55}{60} \text{ h}} = \frac{430 \times 60}{55} \text{ km/h} = 469.09 \text{ km/h}$ (approximately).
6. Question 5
5. A motorcyclist crosses a bridge in 5 seconds at 60 km/h. First, convert 60 km/h to m/s: $v = \frac{60 \text{ km/h}}{3.6} = 16.67 \text{ m/s}$ (approximately). Then, the length of the bridge is $d = v \times t = 16.67 \text{ m/s} \times 5 \text{ s} = 83.33 \text{ m}$ (approximately).
7. Question 6
6. Juma ran 40 m at 8 m/s. The time is $t = \frac{40 \text{ m}}{8 \text{ m/s}} = 5 \text{ s}$.
8. Final Answers
The velocities, distances, and times have been calculated for each scenario. The answers are:
1. a) 20 m/s, b) 72 km/h
2. 10 m/s
3. 9000 km/h
4. 469.09 km/h (approximately)
5. 83.33 m (approximately)
6. 5 s
### Examples
Understanding velocity, distance, and time is crucial in everyday life. For example, when planning a road trip, you need to calculate how long it will take to reach your destination based on the distance and your average speed. Similarly, athletes use these calculations to optimize their performance, and engineers use them to design efficient transportation systems. Knowing these relationships allows for better time management and decision-making in various scenarios.
- Convert m/s to km/h by multiplying by 3.6.
- Convert km/h to m/s by dividing by 3.6.
- Apply the formulas to find the unknown values: $\boxed{v, d, t}$.
### Explanation
1. Understanding the Problem
The problem involves calculating velocities, distances, and times using the formula $velocity = \frac{distance}{time}$. We also need to perform unit conversions between meters, kilometers, seconds, and hours.
2. Question 1
1. A motorist travelled 900 m in 45 seconds.
a) To find the velocity in m/s, we divide the distance by the time: $v = \frac{900 \text{ m}}{45 \text{ s}} = 20 \text{ m/s}$.
b) To convert this to km/h, we multiply by 3.6: $20 \text{ m/s} \times 3.6 = 72 \text{ km/h}$.
3. Question 2
2. An athlete completed a 100 m race in 10 seconds. The velocity is $v = \frac{100 \text{ m}}{10 \text{ s}} = 10 \text{ m/s}$.
4. Question 3
3. A rocket travelled 20 km in 8 seconds. The velocity is $v = \frac{20 \text{ km}}{8 \text{ s}} = 2.5 \text{ km/s}$. To convert to km/h, we multiply by 3600: $2.5 \text{ km/s} \times 3600 = 9000 \text{ km/h}$.
5. Question 4
4. An airplane flew 430 km in 55 minutes. First, convert 55 minutes to hours: $t = \frac{55}{60} \text{ h}$. Then, the velocity is $v = \frac{430 \text{ km}}{\frac{55}{60} \text{ h}} = \frac{430 \times 60}{55} \text{ km/h} = 469.09 \text{ km/h}$ (approximately).
6. Question 5
5. A motorcyclist crosses a bridge in 5 seconds at 60 km/h. First, convert 60 km/h to m/s: $v = \frac{60 \text{ km/h}}{3.6} = 16.67 \text{ m/s}$ (approximately). Then, the length of the bridge is $d = v \times t = 16.67 \text{ m/s} \times 5 \text{ s} = 83.33 \text{ m}$ (approximately).
7. Question 6
6. Juma ran 40 m at 8 m/s. The time is $t = \frac{40 \text{ m}}{8 \text{ m/s}} = 5 \text{ s}$.
8. Final Answers
The velocities, distances, and times have been calculated for each scenario. The answers are:
1. a) 20 m/s, b) 72 km/h
2. 10 m/s
3. 9000 km/h
4. 469.09 km/h (approximately)
5. 83.33 m (approximately)
6. 5 s
### Examples
Understanding velocity, distance, and time is crucial in everyday life. For example, when planning a road trip, you need to calculate how long it will take to reach your destination based on the distance and your average speed. Similarly, athletes use these calculations to optimize their performance, and engineers use them to design efficient transportation systems. Knowing these relationships allows for better time management and decision-making in various scenarios.
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