Metre per second
The metre per second (symbol: m/s or m⋅s⁻¹) is the coherent derived unit of both speed (a scalar quantity) and velocity (a vector quantity specifying magnitude and direction) in the International System of Units (SI).[1] It represents the speed of an object that travels a distance of one metre in one second.[2] This unit is formed by dividing the SI base unit of length, the metre (m), by the SI base unit of time, the second (s).[1] The metre is defined as the distance travelled by light in vacuum during a time interval of 1/299 792 458 of a second, with the speed of light in vacuum fixed exactly at 299 792 458 m/s.[1] The second, in turn, is defined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the caesium-133 atom at rest at 0 K.[1] One metre per second is exactly equivalent to 3.6 kilometres per hour (km/h), derived from the relations 1 kilometre = 1 000 metres and 1 hour = 3 600 seconds.[1] In scientific and engineering contexts, the metre per second is the standard for measuring motion, such as the velocities of particles in high-energy physics experiments, wind speeds in meteorology, or flow rates in fluid dynamics.[3] It also appears in derived units like acceleration (m/s²) and force (newton = kg⋅m/s²), underscoring its foundational role in SI coherence.[1] While everyday applications often favour units like kilometres per hour or miles per hour for vehicle speeds, the metre per second ensures precision in technical fields without needing conversion factors.[2]Fundamentals
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 [L T^{-1}], where L represents the dimension of length and T 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 \frac{ds}{dt} where s 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 (c \approx 3 \times 10^8 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.[10] 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).[11] 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.[12] To convert from m/s to ft/s, multiply by approximately 3.28084, as derived from the foot-metre relation:$1 \, \mathrm{m/s} = \frac{1}{0.3048} \, \mathrm{ft/s} \approx 3.28084 \, \mathrm{ft/s} (exact).[10] For miles per hour, the conversion factor is approximately 2.23694, based on the mile-metre and hour-second relations:
$1 \, \mathrm{m/s} = \frac{3600}{1609.344} \, \mathrm{mi/h} \approx 2.23694 \, \mathrm{mi/h} (exact).[10]
| 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. [10] |
| 1 m/s | mi/h | 2.236936292 | Exact; common for road speeds and aviation. [10] |
| 1 m/s | Knot (kn) | 1.943844492 | Exact; nautical mile (1852 m) per hour. [10] |