Lesson Word problems on units conversion

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Word problems on units conversion


Problem 1. Acceleration


Gravity acceleration at the Earth surface is 9.81 m%2Fs%5E2.
How much is this in ft%2Fs%5E2? In in%2Fs%5E2?
Solution
1 ft = 0.3048 m (see, for example, the units converter, or any appropriate handbook, textbook, or the Internet web-site).
So, 1 m = 1/0.3048 ft = 3.2808 ft = 12*3.2808 in = 39.37 in.
Therefore, 9.81 m%2Fs%5E2 = 9.81 * 3.2808 ft%2Fs%5E2 = 32.19 ft%2Fs%5E2.
Further, because 1 ft = 12 in, we have
9.81 m%2Fs%5E2 = 32.19 ft%2Fs%5E2 = 32.19 *12 in%2Fs%5E2 = 386.2 in%2Fs%5E2.
Answer. Gravity acceleration at the Earth surface is 9.81 m%2Fs%5E2, or 32.19 ft%2Fs%5E2, or 386.2 in%2Fs%5E2.

Problem 2. Speed


Car A makes 100 miles per hour, car B makes 120 kilometers per hour.
Which car is moving with larger speed?

Solution
To compare speed of these two cars, let's convert the speed of car A to km%2Fh.
1 mile = 1609 m = 1.609 km (see, for example, the unit converter under this topic).
So, the car's A speed is 100 miles%2Fh = 100*1.609 km%2Fh = 160.9 km%2Fh.

Answer. Car A is moving faster than car B.

Problem 3. Flow


The water supply well produces 18 gallons of water per minute from the subsurface aquifer.
How much is the flow rate in cubic meters per hour?

Solution
1 gallon(US Liquid) is equal to 0.003785 m%5E3 (or 3.785 liters).
Hence, 18 gallons/min = 18*0.003785 m%5E3%2Fmin = 18*0.003785*60 m%5E3%2Fh = 4.0878 m%5E3%2Fh.
Answer. The flow rate is 4.0878 m%5E3%2Fh.

Problem 4. Temperature


The Death Valley in the Eastern California is the hottest place in the Western hemisphere with the highest measured temperature record of 134 °F (degree of Fahrenheit).
The world record is 57.8 °C (degree of Celsius) in Al 'Aziziyah, Libya.
Compare these two temperature records.

Solution
To compare these two temperature records, let's express 134 °F in Celsius using the conversion formula from Fahrenheit to Celsius
T%5BC%5D=%28T%5BF%5D-32%29%2A5%2F9.
Substituting T%5BF%5D=134 °F to this formula, we have for temperature of Death Valley
T=%28134-32%29%2A5%2F9=+56.67 °C.
So, the highest temperature in the Death Valley is 56.67 °C against 57.8 °C in Al 'Aziziyah, Libya.
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