Speed

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Speed
Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a given amount of time, while a slow-moving object covers a relatively small amount of distance in the same amount of time.
Common symbols
v
SI unit m/s, m s−1
Dimension LT−1

In everyday use and in kinematics, the speed (commonly referred to as v) of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity. [1] The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; [2] the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is the magnitude of velocity (a vector), which indicates additionally the direction of motion.

Contents

Speed has the dimensions of distance divided by time. The SI unit of speed is the metre per second (m/s), but the most common unit of speed in everyday usage is the kilometre per hour (km/h) or, in the US and the UK, miles per hour (mph). For air and marine travel, the knot is commonly used.

The fastest possible speed at which energy or information can travel, according to special relativity, is the speed of light in vacuum c = 299792458 metres per second (approximately 1079000000 km/h or 671000000 mph). Matter cannot quite reach the speed of light, as this would require an infinite amount of energy. In relativity physics, the concept of rapidity replaces the classical idea of speed.

Definition

Historical definition

Italian physicist Galileo Galilei is usually credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time. [3] In equation form, that is

where ${\displaystyle v}$ is speed, ${\displaystyle d}$ is distance, and ${\displaystyle t}$ is time. A cyclist who covers 30 metres in a time of 2 seconds, for example, has a speed of 15 metres per second. Objects in motion often have variations in speed (a car might travel along a street at 50 km/h, slow to 0 km/h, and then reach 30 km/h).

Instantaneous speed

Speed at some instant, or assumed constant during a very short period of time, is called instantaneous speed. By looking at a speedometer, one can read the instantaneous speed of a car at any instant. [3] A car travelling at 50 km/h generally goes for less than one hour at a constant speed, but if it did go at that speed for a full hour, it would travel 50 km. If the vehicle continued at that speed for half an hour, it would cover half that distance (25 km). If it continued for only one minute, it would cover about 833 m.

In mathematical terms, the instantaneous speed ${\displaystyle v}$ is defined as the magnitude of the instantaneous velocity ${\displaystyle {\boldsymbol {v}}}$, that is, the derivative of the position ${\displaystyle {\boldsymbol {r}}}$ with respect to time: [2] [4]

${\displaystyle v=\left|{\boldsymbol {v}}\right|=\left|{\dot {\boldsymbol {r}}}\right|=\left|{\frac {d{\boldsymbol {r}}}{dt}}\right|\,.}$

If ${\displaystyle s}$ is the length of the path (also known as the distance) travelled until time ${\displaystyle t}$, the speed equals the time derivative of ${\displaystyle s}$: [2]

${\displaystyle v={\frac {ds}{dt}}.}$

In the special case where the velocity is constant (that is, constant speed in a straight line), this can be simplified to ${\displaystyle v=s/t}$. The average speed over a finite time interval is the total distance travelled divided by the time duration.

Average speed

Different from instantaneous speed, average speed is defined as the total distance covered divided by the time interval. For example, if a distance of 80 kilometres is driven in 1 hour, the average speed is 80 kilometres per hour. Likewise, if 320 kilometres are travelled in 4 hours, the average speed is also 80 kilometres per hour. When a distance in kilometres (km) is divided by a time in hours (h), the result is in kilometres per hour (km/h).

Average speed does not describe the speed variations that may have taken place during shorter time intervals (as it is the entire distance covered divided by the total time of travel), and so average speed is often quite different from a value of instantaneous speed. [3] If the average speed and the time of travel are known, the distance travelled can be calculated by rearranging the definition to

${\displaystyle d={\boldsymbol {\bar {v}}}t\,.}$

Using this equation for an average speed of 80 kilometres per hour on a 4-hour trip, the distance covered is found to be 320 kilometres.

Expressed in graphical language, the slope of a tangent line at any point of a distance-time graph is the instantaneous speed at this point, while the slope of a chord line of the same graph is the average speed during the time interval covered by the chord. Average speed of an object is Vav = s÷t

Difference between speed and velocity

Speed denotes only how fast an object is moving, whereas velocity describes both how fast and in which direction the object is moving. [5] If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified.

The big difference can be discerned when considering movement around a circle. When something moves in a circular path and returns to its starting point, its average velocity is zero, but its average speed is found by dividing the circumference of the circle by the time taken to move around the circle. This is because the average velocity is calculated by considering only the displacement between the starting and end points, whereas the average speed considers only the total distance travelled.

Tangential speed

Tangential speed is the speed of an object undergoing circular motion, i.e., moving along a circular path. [6] A point on the outside edge of a merry-go-round or turntable travels a greater distance in one complete rotation than a point nearer the center. Travelling a greater distance in the same time means a greater speed, and so linear speed is greater on the outer edge of a rotating object than it is closer to the axis. This speed along a circular path is known as tangential speed because the direction of motion is tangent to the circumference of the circle. For circular motion, the terms linear speed and tangential speed are used interchangeably, and both use units of m/s, km/h, and others.

Units

Units of speed include:

Conversions between common units of speed
m/s km/h mph (mi/h) knot fps (ft/s)
1 m/s = 13.6000002.236936*1.943844*3.280840*
1 km/h = 0.277778*10.621371*0.539957*0.911344*
1 mph (mi/h) = 0.447041.60934410.868976*1.466667*
1 knot = 0.514444*1.8521.150779*11.687810*
1 fps (ft/s) = 0.30481.097280.681818*0.592484*1

(* = approximate values)

Examples of different speeds

Speedm/sft/skm/hmphNotes
Global average sea level rise 0.000000000110.000000000360.00000000040.000000000253.5 mm/year [7]
Approximate rate of continental drift 0.00000000130.00000000420.00000000450.00000000284 cm/year. Varies depending on location.
Speed of a common snail 0.0010.0030.0040.0021 millimetre per second
A brisk walk 1.75.56.13.8
A typical road cyclist4.414.41610Varies widely by person, terrain, bicycle, effort, weather
A fast martial arts kick7.725.227.717.2Fastest kick recorded at 130 milliseconds from floor to target at 1 meter distance. Average velocity speed across kick duration [8]
Sprint runners 12.24043.9227 Usain Bolt's 100 metres world record.
Approximate average speed of road race cyclists12.541.04528On flat terrain, will vary
Typical suburban speed limit in most of the world13.845.35030
Taipei 101 observatory elevator16.754.860.637.61010 m/min
Typical rural speed limit24.680.6688.556
British National Speed Limit (single carriageway)26.88896.5660
Category 1 hurricane3310811974Minimum sustained speed over one minute
Average peak speed of a cheetah33.53110120.775
Speed limit on a French autoroute 36.111813081
Highest recorded human-powered speed37.02121.5133.282.8 Sam Whittingham in a recumbent bicycle [9]
Average speed of Human sneeze44.44145.8216099.42
Muzzle velocity of a paintball marker 90295320200
Cruising speed of a Boeing 747-8 passenger jet255836917570 Mach 0.85 at 35000 ft (10668 m) altitude
Speed of a .22 caliber Long Rifle bullet326.1410701174.09729.55
The official land speed record 341.11119.11227.98763
The speed of sound in dry air at sea-level pressure and 20 °C34311251235768 Mach 1 by definition. 20 °C = 293.15  kelvins.
Muzzle velocity of a 7.62×39mm cartridge710233026001600The 7.62×39mm round is a rifle cartridge of Soviet origin
Official flight airspeed record for jet engined aircraft980321535302194 Lockheed SR-71 Blackbird
Space Shuttle on re-entry7800256002800017,500
Escape velocity on Earth1120036700400002500011.2 km·s−1
Voyager 1 relative velocity to the Sun in 201317000558006120038000Fastest heliocentric recession speed of any humanmade object. [10] (11 mi/s)
Average orbital speed of planet Earth around the Sun297839771310721866623
The fastest recorded speed of the Helios probes 70,220230,381252,792157,078Recognized as the fastest speed achieved by a man-made spacecraft, achieved in solar orbit.
Orbital speed of the Sun relative to the center of the galaxy251000823000904000561000
Speed of the Galaxy relative to the CMB 550000180000020000001240000
Speed of light in vacuum (symbol c)2997924589835710561079252848670616629Exactly 299792458 m/s, by definition of the metre
Speedm/sft/skm/hmphNotes

Psychology

According to Jean Piaget, the intuition for the notion of speed in humans precedes that of duration, and is based on the notion of outdistancing. [11] Piaget studied this subject inspired by a question asked to him in 1928 by Albert Einstein: "In what order do children acquire the concepts of time and speed?" [12] Children's early concept of speed is based on "overtaking", taking only temporal and spatial orders into consideration, specifically: "A moving object is judged to be more rapid than another when at a given moment the first object is behind and a moment or so later ahead of the other object." [13]

Related Research Articles

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are vector quantities. The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes:

Frequency, measured in hertz, is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency by a factor of 2π. The period is the interval of time between events, so the period is the reciprocal of the frequency: f = 1/T.

In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity. Power is a scalar quantity.

The speed of light in vacuum, commonly denoted c, is a universal physical constant that is exactly equal to 299,792,458 metres per second. According to the special theory of relativity, c is the upper limit for the speed at which conventional matter or energy can travel through space.

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur.

In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force. It describes the rate of change of angular momentum that would be imparted to an isolated body.

In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically stated as an ideal speed, ignoring atmospheric friction. Although the term "escape velocity" is common, it is more accurately described as a speed than a velocity because it is independent of direction. The escape speed is independent of the mass of the escaping object, but increases with the mass of the primary body; it decreases with the distance from the primary body, thus taking into account how far the object has already traveled. Its calculation at a given distance means that no acceleration is further needed for the object to escape: it will slow down as it travels—due to the massive body's gravity—but it will never quite slow to a stop. On the other hand, an object already at escape speed needs slowing for it to be captured by the gravitational influence of the body.

In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics.

In physics, angular velocity, also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates around an axis of rotation and how fast the axis itself changes direction.

In physics, angular acceleration is the time rate of change of angular velocity. Following the two types of angular velocity, spin angular velocity and orbital angular velocity, the respective types of angular acceleration are: spin angular acceleration, involving a rigid body about an axis of rotation intersecting the body's centroid; and orbital angular acceleration, involving a point particle and an external axis.

In gravitationally bound systems, the orbital speed of an astronomical body or object is the speed at which it orbits around either the barycenter or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.

In mathematics, a rate is the quotient of two quantities in different units of measurement, often represented as a fraction. If the divisor in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically, then the dividend of the rate expresses the corresponding rate of change in the other (dependent) variable. In some cases, it may be regarded as a change to a value, which is caused by a change of a value in respect to another value. For example, acceleration is a change in speed in respect to time

In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass.

Rotational frequency, also known as rotational speed or rate of rotation, is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s−1); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).

In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position.

Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will result.

In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units, the position of the moving object is measured in meters relative to the origin, while the time is measured in seconds. Placing position on the y-axis and time on the x-axis, the slope of the curve is given by:

Linear motion, also called rectilinear motion, is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion, with constant velocity ; and non-uniform linear motion, with variable velocity. The motion of a particle along a line can be described by its position , which varies with (time). An example of linear motion is an athlete running a 100-meter dash along a straight track.

Velocity is the speed in combination with the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

References

1. "Origin of the speed/velocity terminology". History of Science and Mathematics Stack Exchange. Retrieved 12 June 2023. Introduction of the speed/velocity terminology by Prof. Tait, in 1882.
2. Elert, Glenn. "Speed & Velocity". The Physics Hypertextbook. Retrieved 8 June 2017.
3. Hewitt 2006 , p. 42
4. "IEC 60050 - Details for IEV number 113-01-33: "speed"". Electropedia: The World's Online Electrotechnical Vocabulary. Retrieved 2017-06-08.
5. Wilson, Edwin Bidwell (1901). Vector analysis: a text-book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs. Yale bicentennial publications. C. Scribner's Sons. p. 125. hdl:2027/mdp.39015000962285. This is the likely origin of the speed/velocity terminology in vector physics.
6. Hewitt 2007, p. 131
7. NASA's Goddard Space Flight Center. "Satellite sea level observations". Global Climate Change. NASA. Retrieved 20 April 2022.
8. "Improve Kicking Speed for Martial Arts | Get Fast Kicks!". Archived from the original on 2013-11-11. Retrieved 2013-08-14.
9. "The Recumbent Bicycle and Human Powered Vehicle Information Center". Archived from the original on 2013-08-11. Retrieved 2013-10-12.
10. Darling, David. "Fastest Spacecraft" . Retrieved August 19, 2013.
11. Jean Piaget, Psychology and Epistemology: Towards a Theory of Knowledge, The Viking Press, pp. 82–83 and pp. 110–112, 1973. SBN 670-00362-x
12. Siegler, Robert S.; Richards, D. Dean (1979). "Development of Time, Speed, and Distance Concepts" (PDF). Developmental Psychology. 15 (3): 288–298. doi:10.1037/0012-1649.15.3.288.
13. Early Years Education: Histories and Traditions, Volume 1. Taylor & Francis. 2006. p. 164. ISBN   9780415326704.