When working with physical quantities in various scientific and engineering fields, it is essential to understand how to convert units accurately. One such unit conversion involves converting acceleration from femtometers per second squared (fm/s²) to meters per second squared (m/s²). This guide provides a step-by-step approach to converting 31.3 femtometers per second squared (fm/s²) into meters per second squared (m/s²).
What are Femtometers and Meters?
Before delving into the conversion process, it is important to understand the units involved:
- Femtometer (fm): A femtometer is a unit of length in the metric system and represents 10−1510^{-15}10−15 meters. It is typically used to measure extremely small distances, such as the size of atomic nuclei.
- Meter (m): A meter is the base unit of length in the International System of Units (SI). It is used to measure the distance or space between two points in the physical world.
Conversion Factor
To convert femtometers (fm) to meters (m), we use the conversion factor:1 fm=10−15 m1 \, \text{fm} = 10^{-15} \, \text{m}1fm=10−15m
This means that 1 femtometer is equivalent to 10−1510^{-15}10−15 meters.
Step-by-Step Conversion Process
Let us now convert 31.3 femtometers per second squared (fm/s²) to meters per second squared (m/s²).
- Starting Value: The given value is 31.3 femtometers per second squared (fm/s²).
- Apply the Conversion Factor: We know that 1 femtometer equals 10−1510^{-15}10−15 meters. So, to convert femtometers to meters, we multiply the given value by 10−1510^{-15}10−15.31.3 fm/s2×10−15=31.3×10−15 m/s231.3 \, \text{fm/s}^2 \times 10^{-15} = 31.3 \times 10^{-15} \, \text{m/s}^231.3fm/s2×10−15=31.3×10−15m/s2
- Simplify the Expression: The expression simplifies to:31.3×10−15 m/s2=3.13×10−14 m/s231.3 \times 10^{-15} \, \text{m/s}^2 = 3.13 \times 10^{-14} \, \text{m/s}^231.3×10−15m/s2=3.13×10−14m/s2
Final Answer
Thus, the conversion of 31.3 femtometers per second squared (fm/s²) into meters per second squared (m/s²) results in:31.3 fm/s2=3.13×10−14 m/s231.3 \, \text{fm/s}^2 = 3.13 \times 10^{-14} \, \text{m/s}^231.3fm/s2=3.13×10−14m/s2
Conclusion
Converting from femtometers per second squared to meters per second squared involves multiplying the given value by 10−1510^{-15}10−15, as a femtometer is equivalent to 10−1510^{-15}10−15 meters. In this case, 31.3 femtometers per second squared equals 3.13×10−143.13 \times 10^{-14}3.13×10−14 meters per second squared. Understanding unit conversions is vital for ensuring that calculations are correct, especially when dealing with measurements in fields such as particle physics or nanotechnology, where extremely small distances are involved.