Questions and Answers
What is the rate of the car in kilometers per hour?
How do you convert kilometers per hour to kilometers per second?
What does 1/72 kilometers per second approximately equal in meters per second?
Why are rates expressed in kilometers per hour and meters per second preferred over kilometers per second?
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What is the correct conversion of 50 km/h to meters per hour?
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How would you express a travel rate of 150 kilometers in terms of kilometers per second over a total time of 3 hours?
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Which unit conversion makes understanding distance traveled easier?
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What is the equivalent distance in meters if a car moves at a rate of 1/72 km/s for 1 hour?
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What is the main issue with expressing travel speeds in meters per hour?
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Study Notes
Understanding Rate of Travel
- A car travels 150 kilometers in 3 hours.
- Rate can be expressed as distance divided by time: Rate = Distance / Time.
- In this case, Rate = 150 km / 3 hr = 50 kilometers per hour (km/h).
- Keeping units during calculations is crucial for clarity.
Dimensional Analysis
- Converting kilometers per hour to kilometers per second requires understanding the time conversion.
- There are 3,600 seconds in an hour.
- To convert, multiply by the conversion factor:
- 50 km/h = 50 km x (1 hr / 3,600 s) = 50/3,600 km/s.
- This simplifies down to 1/72 kilometers per second.
Evaluation of Units
- 1/72 km/s can be challenging to conceptualize; it equals about 0.0139 km/s.
- Knowing distances in intuitive units (e.g., meters) can enhance understanding.
Conversion to Meters Per Second
- Converting kilometers to meters (1 km = 1,000 m) makes values more relatable.
- 1/72 km/s can be converted:
- 1/72 km/s = (1,000 m / 1 km) x (1/72 km/s) = 1,000/72 m/s.
- This results in approximately 13.9 m/s, a more understandable and useful figure.
Alternative Units Analysis
- Alternative ways to express the rate, such as meters per hour, result in large numbers (50,000 m/h), which may be cumbersome to interpret.
- Describing travel rate in kilometers per hour and meters per second is practical.
- Kilometers per second or meters per hour create unusual contextual understanding.
Summary of Reasonable Units
- Reasonable rates for this travel scenario are:
- 50 kilometers per hour (intuitive for road travel).
- 13.9 meters per second (easier to imagine and visualize).
- Rates expressed in kilometers per second and meters per hour are generally less practical.
Understanding Rate of Travel
- A car covers 150 kilometers in a duration of 3 hours.
- The rate of travel is calculated using the formula: Rate = Distance / Time.
- For this scenario, the rate computes to 50 kilometers per hour (km/h).
- Maintaining unit consistency in calculations enhances clarity and accuracy.
Dimensional Analysis
- To convert km/h to km/s, it's essential first to recognize that there are 3,600 seconds in an hour.
- The conversion process involves multiplying by the proper conversion factor:
- 50 km/h is calculated as 50 km x (1 hr / 3,600 s), resulting in 50/3,600 km/s.
- This fraction simplifies to 1/72 kilometers per second (km/s).
Evaluation of Units
- Understanding 1/72 km/s may be difficult, translating to approximately 0.0139 km/s.
- Relating speeds to more intuitive units, like meters, can facilitate better comprehension.
Conversion to Meters Per Second
- To convert kilometers to meters (1 km equals 1,000 meters), the value becomes more relatable.
- The conversion of 1/72 km/s to meters per second is done as follows:
- 1/72 km/s is calculated as (1,000 m / 1 km) x (1/72 km/s), leading to 1,000/72 m/s.
- This results in approximately 13.9 meters per second (m/s), offering a more understandable figure for speed.
Alternative Units Analysis
- Representing travel rates in meters per hour can generate cumbersome figures, such as 50,000 m/h.
- Kilometers per hour and meters per second offer practical and comprehensible expressions of travel rates.
- Using kilometers per second or meters per hour can sometimes lead to less intuitive understanding of speed.
Summary of Reasonable Units
- Practical rates for this travel context include:
- 50 kilometers per hour, a familiar measure for road travel.
- 13.9 meters per second, which is easier for visualization and understanding.
- Rates expressed in kilometers per second and meters per hour are less practical for everyday interpretation.
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Description
This quiz explores the concepts of rate of travel by examining a car's speed. It covers dimensional analysis and unit conversion, including transforming kilometers per hour to meters per second. Understanding these concepts is essential for practical applications in physics and everyday situations.
