When it comes to measurements in physics, it is often necessary to convert units to make calculations easier or to work with more familiar values. One common conversion involves changing acceleration values from metric units like millimeters per second squared (mm/s²) to imperial units, such as yards per square second (yd/s²). This article will explain how to convert 35.20 mm/s² to yards per square second in a step-by-step manner.
Step 1: Understand the Conversion Factors
To make this conversion, we need to know the relationship between millimeters and yards, since the acceleration in question is given in millimeters per second squared. The key conversion factor here is: 1 yard = 914.4 millimeters (mm).
With this in mind, the next task is to convert millimeters into yards. To convert millimeters to yards, you simply divide the number of millimeters by the conversion factor.
Step 2: Set Up the Conversion Equation
To convert 35.20 mm/s² to yd/s², you use the following equation:Acceleration in yards per square second=Acceleration in millimeters per second squaredMillimeters per yard2\text{Acceleration in yards per square second} = \frac{\text{Acceleration in millimeters per second squared}}{\text{Millimeters per yard}^2}Acceleration in yards per square second=Millimeters per yard2Acceleration in millimeters per second squared
Where:
- Acceleration in millimeters per second squared is 35.20 mm/s².
- The conversion factor for millimeters to yards is 914.4 mm/yard.
Since we are working with squared units (mm² to yd²), we square the conversion factor:(914.4 mm/yard)2=836,257.6 mm2/yd2\left( 914.4 \, \text{mm/yard} \right)^2 = 836,257.6 \, \text{mm}^2/\text{yd}^2(914.4mm/yard)2=836,257.6mm2/yd2
Step 3: Perform the Conversion
Now, plug the values into the equation:Acceleration in yd/s²=35.20 mm/s²836,257.6 mm2/yd2\text{Acceleration in yd/s²} = \frac{35.20 \, \text{mm/s²}}{836,257.6 \, \text{mm}^2/\text{yd}^2}Acceleration in yd/s²=836,257.6mm2/yd235.20mm/s²
Carrying out the division:Acceleration in yd/s²=0.00004206 yd/s²\text{Acceleration in yd/s²} = 0.00004206 \, \text{yd/s²}Acceleration in yd/s²=0.00004206yd/s²
Step 4: Final Answer
After performing the calculation, the acceleration of 35.20 mm/s² is equivalent to approximately 0.00004206 yards per square second.
Conclusion
The process of converting 35.20 mm/s² to yd/s² involves understanding the conversion factor between millimeters and yards, applying it correctly to squared units, and then performing the calculation. The final result, 0.00004206 yd/s², demonstrates how to express acceleration in imperial units. This kind of conversion is important in many scientific and engineering applications, where consistent units are essential for accurate results.