Question

The speed limit on a particular stretch of road is 45 miles per hour. Express this speed limit in millifurlongs per microfortnight. A furlong is \(\frac{1}{8}\) mile, and a fortnight is a period of 2 weeks.

Short answer

Question: Convert the speed limit of 45 miles per hour to millifurlongs per microfortnight. Answer: Approximately 5,580,357.14 millifurlongs per microfortnight.

Step-by-step solution

Convert miles to millifurlongs

Given 1 mile equals to \(\frac{1}{8}\) furlong, and we want to find the value in millifurlongs. We know that 1 furlong = 1000 millifurlongs. So, to convert 45 miles to millifurlongs, we'll use the following conversion factors: 45 miles * \(\frac{1}{8}\) furlongs/mile * 1000 millifurlongs/furlong

Convert hours to microfortnights

We need to convert hours to fortnights and then to microfortnights. We know that 1 fortnight = 2 weeks, and 1 week = 168 hours (assuming 24 hours in a day and 7 days in a week). Also, we know that 1 fortnight = \(10^6\) microfortnights. So, we'll use the following conversion factors: 1 hour * \(\frac{1}{168 \times 2}\) fortnights/hour * \(10^6\) microfortnights/fortnight

Calculate the speed in millifurlongs per microfortnight

Now, we multiply the converted distance and time to get the speed in millifurlongs per microfortnight: 45 miles/hour * \(\frac{1}{8}\) furlongs/mile * 1000 millifurlongs/furlong * \(\frac{1}{168 \times 2}\) fortnights/hour * \(10^6\) microfortnights/fortnight After performing the calculation: Speed = 45 * \(\frac{1}{8}\) * 1000 * \(\frac{1}{336}\) * \(10^6\) millifurlongs per microfortnight Speed ≈ 5,580,357.14 millifurlongs per microfortnight So, the speed limit of 45 miles per hour is approximately 5,580,357.14 millifurlongs per microfortnight.

Key concepts

Dimensional Analysis

Dimensional analysis is a powerful tool used in physics and engineering to convert one set of units to another and to check the plausibility of equations. This technique involves multiplying the quantity to be converted by one or more 'conversion factors,' which are ratios of equivalent measurements that equal one. The key is to set up these factors so that units you want to eliminate are canceled out.

For instance, when converting speed from miles per hour to millifurlongs per microfortnight, as in our example exercise, the solution takes advantage of dimensional analysis. By systematically applying conversions of distance and time, we can transition between units seamlessly while ensuring unit consistency and equation balance. This process fosters a deeper understanding of the fundamental relationship between different measurements and reassures the accuracy of our calculations.

Units of Measurement

Units of measurement are standardized quantities used to express and compare physical quantities. Examples include meters and feet for length, seconds and hours for time, and grams and pounds for weight. Different systems of measurement exist globally, with the International System of Units (SI) being the most widely adopted. Certain fields, like navigation and land measurement, still use customary units such as furlongs and nautical miles.

Understanding various units of measurement is crucial for students, as they often encounter situations requiring conversion from one system to another. For example, in the solution for our exercise, we convert miles to furlongs and then to millifurlongs. Having a firm grasp of what these units represent and how they relate to each other enriches a student's practical problem-solving abilities.

Speed Conversion

Speed conversion involves changing the expression of a speed value from one set of distance and time units to another. Practicing this type of conversion is essential because it helps students understand the relative motion and how different units of speed interrelate. In our exercise, we converted miles per hour to millifurlongs per microfortnight, an unconventional unit. This process underscores the concept that speed remains constant despite changing the units of measurement; the physical phenomenon it represents doesn't falter.

What Steps to Take for Speed Conversion

First, determine the conversion factors for the distance and time units. Next, multiply the given speed by those factors, ensuring that unwanted units cancel out while desired units remain. Finally, execute the calculation to get the speed in the new units. This process is vital for clear scientific communication, ensuring consistency and understanding across various fields and applications.