Metre per second
View on Wikipedia| Metre per second | |
|---|---|
| Unit system | SI |
| Unit of | speed |
| Symbol | m/s |
| Conversions | |
| 1 m/s in ... | ... is equal to ... |
| km/h | 3.6 |
| mph | 2.2369 |
| kn | 1.9438 |
| ft/s | 3.2808 |
The metre per second is the unit of both speed (a scalar quantity) and velocity (a vector quantity, which has direction and magnitude) in the International System of Units (SI), equal to the speed of a body covering a distance of one metre in a time of one second. As the base unit for speed in the SI, it is commonly used in physics, mechanics, and engineering contexts. It represents both scalar speed and vector velocity, depending on context. According to the definition of metre,[1] 1 m/s is exactly of the speed of light.

The SI unit symbols are m/s, m·s−1, m s−1, or m/s.[2]
Conversions
[edit]1 m/s is equivalent to:
- = 3.6 km/h (exactly)[3]
- ≈ 3.2808 feet per second (approximately)[4]
- ≈ 2.2369 miles per hour (approximately)[5]
- ≈ 1.9438 knots (approximately)[6]
1 foot per second = 0.3048 m/s (exactly)[7]
1 mile per hour = 0.44704 m/s (exactly)[8]
History and Standardization
[edit]The metre per second became the official SI derived unit for both speed and velocity with the establishment of the International System of Units (SI) in 1960 by the General Conference on Weights and Measures (CGPM).[10] Prior to this, various units such as feet per second, miles per hour, and knots were more commonly used, depending on the region and application.
The unit derives from the SI base units of metre (length) and second (time), both of which were defined more precisely in the 20th century. The metre was originally based on the dimensions of the Earth, but is now defined by the distance light travels in a vacuum in 1/299,792,458 of a second. The second is defined using the vibration frequency of caesium atoms (9,192,631,770 oscillations per second).[11] Because of its accuracy, simplicity and preciseness, this unit is adopted as the official unit of speed and velocity and is almost always used as the unit of speed and velocity in scientific occasions.
Relation to other measures
[edit]The benz, named in honour of Karl Benz, has been proposed as a name for one metre per second.[12] Although it has seen some support as a practical unit,[13] primarily from German sources,[12] it was rejected as the SI unit of velocity[14] and has not seen widespread use or acceptance.[15]
The square of metres per second, or square metre per square second, is used as a unit of gravitational potential.
Unicode character
[edit]See also
[edit]References
[edit]- ^ "Definitions of the SI base units". physics.nist.gov. 29 May 2019. Retrieved 8 February 2022.
- ^ "SI brochure, Section 5.1". Archived from the original on 2019-03-21. Retrieved 2018-06-08.
- ^ CDX Automotive (2013). South African Automotive Light Vehicle Level 3. Jones & Bartlett Learning. p. 478. ISBN 978-1449697853.
- ^ Dinçer, İbrahim; Rosen, Marc A. (2007). EXERGY: Energy, Environment and Sustainable Development. Amsterdam: Elsevier. p. 444. ISBN 9780080531359. OCLC 228148217.
- ^ Jazar, Reza N. (2017). Vehicle Dynamics: Theory and Application (3. ed.). Cham, Switzerland: Springer. p. 957. ISBN 9783319534411. OCLC 988750637.
- ^ Collinson, R.P.G. (2013). Introduction to Avionics Systems (2. ed.). Boston: Springer Science & Business Media. p. 16. ISBN 9781441974662. OCLC 861706692.
- ^ Potter, Merle C; Wiggert, David C; Ramadan, Bassem H. (2016). Mechanics of Fluids, SI Edition (5. ed.). Cengage Learning. p. 722. ISBN 978-1305887701.
- ^ Das, Braja M.; Kassimali, Aslam; Sami, Sedat (2010). Mechanics for Engineers: Statics. Ft. Lauderdale, FL: J. Ross Publishing. p. 556. ISBN 9781604270297. OCLC 419827343.
- ^ Wright, Gus (2015). Fundamentals of medium/heavy duty diesel engines. Burlington, Massachusetts: Jones & Bartlett Publishers. p. 1349. ISBN 9781284067057. OCLC 927104266.
- ^ "SI Brochure - BIPM". BIPM. Archived from the original on 2025-06-24. Retrieved 2025-07-04.
- ^ "Second | COSMOS". astronomy.swin.edu.au. Retrieved 2025-07-04.
- ^ a b Klein HA. (2011). The Science of Measurement: A Historical Survey. Dover Publications. p. 695. ISBN 978-0486258393.
- ^ Heijungs R. (2005). "On the Use of Units in LCA". The International Journal of Life Cycle Assessment. 10 (3): 174. Bibcode:2005IJLCA..10..173H. doi:10.1065/lca2005.02.199. S2CID 110961104.
- ^ Cardarelli F. (2004). Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins. Transl. by MJ Shields. (3rd revised ed.). Springer. p. 217. ISBN 978-1852336820.
- ^ Dresner S. (1974). Units of Measurement: An Encyclopaedic Dictionary of Units Both Scientific and Popular and the Quantities They Measure. Harvey Miller and Medcalf. p. 13. ISBN 978-0-85602-036-0.
- ^ Unicode Consortium (2019). "The Unicode Standard 12.0 – CJK Compatibility ❰ Range: 3300—33FF ❱" (PDF). Unicode.org. Retrieved May 24, 2019.
External links
[edit]Metre per second
View on GrokipediaFundamentals
Definition
The metre per second (symbol: m/s) is the coherent SI derived unit of speed, defined as the speed of a body covering a distance of one metre in one second.[1] It is a composite unit derived from the base SI units of length (metre) and time (second), expressed as m/s or m·s⁻¹, with no prefix multipliers or numerical factors other than unity in its base form.[1][4] The metre per second quantifies both speed, a scalar quantity representing the rate of motion irrespective of direction, and velocity, a vector quantity that includes directional information, particularly in one-dimensional contexts.[1] Its dimensional formula is , where represents the dimension of length and the dimension of time.[1]Physical Significance
In physics, the metre per second (m/s) represents the rate of change of position with respect to time, serving as a fundamental measure in kinematics for quantifying motion. As a derived SI unit, it encapsulates the displacement in metres divided by the duration in seconds, enabling precise descriptions of both scalar speed and vector velocity.[4] In mechanics, m/s finds essential applications in calculating average speed, defined as total distance traveled divided by elapsed time, and instantaneous velocity, expressed as the derivative where is position as a function of time.[5] These uses underpin analyses of projectile motion and everyday phenomena like vehicle travel, providing a standardized metric for predicting and modeling trajectories.[6] Representative examples illustrate its scale in natural processes: the escape velocity from Earth's surface, the minimum speed required to overcome gravitational pull without further propulsion, is approximately 11.2 km/s, highlighting m/s-based units for high-energy astrophysical contexts.[7] Similarly, the speed of sound in dry air at sea level and 20°C is about 343 m/s, a benchmark for acoustic wave propagation in atmospheric physics.[8] The m/s unit is integral to non-relativistic regimes in relativity, where speeds far below the speed of light ( m/s) are analyzed using classical approximations, and in fluid dynamics, where it quantifies flow velocities in equations governing viscosity and turbulence.[9] Its adoption stems from the SI system's coherence, ensuring decimal-based conversions and universal precision in international scientific collaboration, unlike inconsistent customary units.[3]Conversions
To Other SI Units
The metre per second (m/s) is the coherent SI derived unit for speed and velocity, formed from the base units of length (metre) and time (second). Other SI units for expressing speed include decimal multiples and submultiples formed by attaching SI prefixes to the metre, such as the kilometre per second (km/s = 10³ m/s) for large-scale speeds in astronomy or physics, the centimetre per second (cm/s = 10⁻² m/s) for smaller velocities in fluid dynamics or microscopy, and the millimetre per second (mm/s = 10⁻³ m/s) for precision measurements in engineering. These prefixed units maintain coherence within the SI system when used with the second, allowing direct scaling without additional factors.[1] An important non-coherent unit accepted for use with the SI is the kilometre per hour (km/h), commonly employed for road vehicle speeds and aviation in many countries. The conversion between m/s and km/h is given by 1 km/h = (1000 m)/(3600 s) = 5/18 m/s, or equivalently, 1 m/s = 18/5 km/h = 3.6 km/h. This factor arises from the definitions of the kilometre (10³ m) and the hour (3600 s), both compatible with SI base units. For example, a speed of 25 m/s equals 90 km/h, illustrating practical equivalence in everyday contexts.[1] The following table summarizes key conversions from m/s to other SI-compatible units for speed:| Unit | Symbol | Conversion Factor to m/s | Example Usage Context |
|---|---|---|---|
| Kilometre per second | km/s | 1 km/s = 1000 m/s | Cosmic velocities, e.g., orbital speeds |
| Centimetre per second | cm/s | 1 cm/s = 0.01 m/s | Microfluidics or particle tracking |
| Millimetre per second | mm/s | 1 mm/s = 0.001 m/s | Machining tolerances or seismic waves |
| Kilometre per hour | km/h | 1 km/h = 1/3.6 m/s ≈ 0.2778 m/s | Traffic regulations, weather reporting |
To Imperial and US Customary Units
The metre per second (m/s) is converted to Imperial and US Customary units of speed primarily through established length and time conversion factors defined by international standards.[https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8] These units include feet per second (ft/s) and miles per hour (mi/h), which are commonly used in engineering, aviation, and automotive contexts in countries employing these systems. The conversions rely on the exact definitions: 1 foot = 0.3048 metre (exact) and 1 (statute) mile = 1609.344 metres (exact), with 1 hour = 3600 seconds (exact).[https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-4-unit-conversion-factors#Section4-1-1] Note that Imperial and US Customary systems align for these speed units, using the international yard and mile, though historical variations existed prior to 1959 standardization.[https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors] To convert from m/s to ft/s, multiply by approximately 3.28084, as derived from the foot-metre relation:| SI Unit (m/s) | Imperial/US Customary Unit | Conversion Factor (m/s to unit) | Notes |
|---|---|---|---|
| 1 m/s | ft/s | 3.280839895 | Exact; used in fluid dynamics and ballistics. [https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8] |
| 1 m/s | mi/h | 2.236936292 | Exact; common for road speeds and aviation. [https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8] |
| 1 m/s | Knot (kn) | 1.943844492 | Exact; nautical mile (1852 m) per hour. [https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8] |