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. (A microfortnight is in fact used as a unit in a particular type of computing system called the VMS system.)

Short answer

Question: Convert 45 miles per hour to millifurlongs per microfortnight. Answer: Approximately 1,071,429 millifurlongs per microfortnight.

Step-by-step solution

Convert the speed from miles to furlongs

To convert the given speed from miles to furlongs, we use the conversion factor: 1 mile = 8 furlongs. The given speed is 45 miles per hour. So, multiplying by the conversion factor, we get: $$ 45 \text{ miles per hour} \times \frac{8 \text{ furlongs}}{1 \text{ mile}} = 45 \times 8 \text{ furlongs per hour} = 360 \text{ furlongs per hour} $$

Convert hours to microfortnights

Now, we need to convert hours to microfortnights. We know that a fortnight is 2 weeks, and that 1 week has 168 hours (24 hours per day and 7 days per week). Therefore, 1 fortnight has 336 hours. So, we have the conversion factor: $$ 1 \text{ fortnight} = 336 \text{ hours} $$ We also know that 1 microfortnight is a millionth (1/1,000,000) of a fortnight. So, we have: $$ 1 \text{ microfortnight} = \frac{1}{1,000,000} \times 336 \text{ hours} $$ Now we need to find the inverse of this conversion factor, which will give us the number of microfortnights per hour: $$ \frac{1}{1 \text{ microfortnight}} = \frac{1,000,000}{336} \text{ hours} $$ Thus, there are \(\frac{1,000,000}{336}\) microfortnights in 1 hour.

Convert the speed from furlongs per hour to millifurlongs per microfortnight

To complete the conversion, we'll multiply the speed in furlongs per hour by the number of microfortnights per hour. $$ 360 \text{ furlongs per hour} \times \frac{1,000,000}{336} \text{ microfortnights per hour} = 360 \times \frac{1,000,000}{336} \text{ millifurlongs per microfortnight} $$ Now, we simply need to do the math: $$ 360 \times \frac{1,000,000}{336} \approx 1,071,429 \text{ millifurlongs per microfortnight} $$ So, the speed limit of 45 miles per hour is approximately equal to 1,071,429 millifurlongs per microfortnight.

Key concepts

Speed Conversion

Understanding speed conversion in physics is critical when dealing with multiple unit systems or attempting to compare two speeds described in different units. Speed, essentially the rate at which an object covers distance, can be expressed in various units such as miles per hour (mph), kilometers per hour (km/h), or even the more unusual millifurlongs per microfortnight.

To convert speed, one should have a clear understanding of the relationship between the units involved. For instance, when converting from miles per hour to furlongs per hour, as seen in the exercise, we utilize the known conversion factor (1 mile = 8 furlongs). Multiplication or division is then used depending on whether you are converting to a larger or smaller unit. Remember, converting to a larger unit (miles to furlongs) involves multiplication, whereas converting to a smaller unit (furlongs to miles) involves division.

Speed Conversion Formula

If the speed is given in unit A and the conversion factor to unit B is C, the formula to get speed in unit B is: \( \text{Speed in unit B} = \text{Speed in unit A} \times C \). Keep your conversion factors handy to easily switch between units and communicate speed in the desired format.

Furlong to Mile Conversion

Conversion from furlongs to miles or vice versa is essential when dealing with distances in different historical or geographical contexts. A furlong is an older unit of length, traditionally used in horse racing and originating from the farming land measurement systems. It is equivalent to \( \frac{1}{8} \) of a mile.

When converting furlongs to miles, it is generally a straightforward division because 1 furlong is a fraction of a mile. As seen in the exercise, the conversion is simply done by acknowledging that 1 mile equals 8 furlongs. So, to convert furlongs to miles, you divide the number of furlongs by 8. Conversely, to convert miles to furlongs, you multiply the number of miles by 8.

Practical Application

This type of conversion may seem obscure, but it actually enhances comprehension of different measurement systems and illustrates the wonderful diversity of units that can be used to measure the same quantity—the distance.

Time Unit Conversion

Time unit conversion is crucial in fields varying from physics to history, as it enables us to comprehend and measure the passage of time in different units. Time can be expressed in seconds, minutes, hours, days, weeks, and even more unusual units like fortnights or microfortnights.

In the given exercise, we see a conversion from hours to microfortnights. A fortnight, which is commonly used in the UK, is equal to 14 days or 2 weeks. Since there are 24 hours in a day, we calculate that there are 336 hours in a fortnight. Calculating microfortnights means dividing this time by one million, as 'micro' is the SI prefix for one millionth.

Understanding SI Prefixes

Understanding prefixes like 'micro' is vital as they're commonly used in various scientific fields. They represent powers of 10 and provide a clear indication of the scale of a unit. When dealing with conversion between standard time units and those modified by SI prefixes, it's important to multiply or divide by the corresponding factor of 10 associated with the prefix.