# Speed

Last updated

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 not the same as velocity.

## 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 a 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

Linear speed is the distance travelled per unit of time, while tangential speed (or tangential velocity) is the linear speed of something 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.

Rotational speed (or angular speed) involves the number of revolutions per unit of time. All parts of a rigid merry-go-round or turntable turn about the axis of rotation in the same amount of time. Thus, all parts share the same rate of rotation, or the same number of rotations or revolutions per unit of time. It is common to express rotational rates in revolutions per minute (RPM) or in terms of the number of "radians" turned in a unit of time. There are little more than 6 radians in a full rotation (2π radians exactly). When a direction is assigned to rotational speed, it is known as rotational velocity or angular velocity. Rotational velocity is a vector whose magnitude is the rotational speed.

Tangential speed and rotational speed are related: the greater the RPMs, the larger the speed in metres per second. Tangential speed is directly proportional to rotational speed at any fixed distance from the axis of rotation. [6] However, tangential speed, unlike rotational speed, depends on radial distance (the distance from the axis). For a platform rotating with a fixed rotational speed, the tangential speed in the centre is zero. Towards the edge of the platform the tangential speed increases proportional to the distance from the axis. [7] In equation form:

${\displaystyle v\propto \!\,r\omega \,,}$

where v is tangential speed and ω (Greek letter omega) is rotational speed. One moves faster if the rate of rotation increases (a larger value for ω), and one also moves faster if movement farther from the axis occurs (a larger value for r). Move twice as far from the rotational axis at the centre and you move twice as fast. Move out three times as far, and you have three times as much tangential speed. In any kind of rotating system, tangential speed depends on how far you are from the axis of rotation.

When proper units are used for tangential speed v, rotational speed ω, and radial distance r, the direct proportion of v to both r and ω becomes the exact equation

${\displaystyle v=r\omega \,.}$

Thus, tangential speed will be directly proportional to r when all parts of a system simultaneously have the same ω, as for a wheel, disk, or rigid wand.

## Units

Units of speed include:

Conversions between common units of speed
m/s km/h mph knot 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 = 0.447041.60934410.868976*1.466667*
1 knot = 0.514444*1.8521.150779*11.687810*
1 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 [8]
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 [9]
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 1 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 [10]
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. [11] (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

## 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. [12] 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?" [13] 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." [14]

## Related Research Articles

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. 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:

In physics, angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, frisbees rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it.

In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

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.

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.

In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. It represents the capability of a force to produce change in the rotational motion of the body. The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "Give me a lever and a place to stand and I will move the Earth". Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Torque is defined as the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.

In physics, angular velocity or rotational velocity, also known as angular frequency vector, is a pseudovector representation of how fast the angular position or orientation of an object changes with time. The magnitude of the pseudovector represents the angular speed, the rate at which the object rotates or revolves, and its direction is normal to the instantaneous plane of rotation or angular displacement. The orientation of angular velocity is conventionally specified by the right-hand rule.

In physics, angular acceleration refers to the time rate of change of angular velocity. As there are two types of angular velocity, namely spin angular velocity and orbital angular velocity, there are naturally also two types of angular acceleration, called spin angular acceleration and orbital angular acceleration respectively. Spin angular acceleration refers to the angular acceleration of a rigid body about its centre of rotation, and orbital angular acceleration refers to the angular acceleration of a point particle about a fixed origin.

In physics, angular frequency"ω" is a scalar measure of rotation rate. It refers to the angular displacement per unit time or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument of the sine function. Angular frequency is the magnitude of the vector quantity angular velocity.

In mathematics, a rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities, and if it is assumed that this quantity can be changed systematically, then the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable.

In physics, a rigid body is a solid body in which deformation is zero or so small it can be neglected. 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.

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. In circular motion, the distance between the body and a fixed point on the surface remains the same.

Rotational speed, of an object rotating around an axis is the number of turns of the object divided by time, specified as revolutions per minute (rpm), cycles per second (cps), radians per second (rad/s), etc.

A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as an accelerating or rotating reference frame. It is related to Newton's second law of motion, which treats forces for just one object.

Rolling is a type of motion that combines rotation and translation of that object with respect to a surface, such that, if ideal conditions exist, the two are in contact with each other without sliding.

In physics, the Thomas precession, named after Llewellyn Thomas, is a relativistic correction that applies to the spin of an elementary particle or the rotation of a macroscopic gyroscope and relates the angular velocity of the spin of a particle following a curvilinear orbit to the angular velocity of the orbital motion.

Rotation around a fixed axis is a special case of rotational motion. The fixed-axis hypothesis excludes the possibility of an axis 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 appear.

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 or zero acceleration; and non-uniform linear motion with variable velocity or non-zero acceleration. 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 100m along a straight track.

Velocity is the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

## References

• Richard P. Feynman, Robert B. Leighton, Matthew Sands. The Feynman Lectures on Physics, Volume I, Section 8–2. Addison-Wesley, Reading, Massachusetts (1963). ISBN   0-201-02116-1.
1. 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.
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 (2006), p. 131
7. Hewitt (2006), p. 132
8. NASA's Goddard Space Flight Center. "Satellite sea level observations". Global Climate Change. NASA. Retrieved 20 April 2022.
9. "Improve Kicking Speed for Martial Arts | Get Fast Kicks!". Archived from the original on 2013-11-11. Retrieved 2013-08-14.
10. "The Recumbent Bicycle and Human Powered Vehicle Information Center". Archived from the original on 2013-08-11. Retrieved 2013-10-12.
11. Darling, David. "Fastest Spacecraft" . Retrieved August 19, 2013.
12. 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
13. 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.
14. Early Years Education: Histories and Traditions, Volume 1. Taylor & Francis. 2006. p. 164. ISBN   9780415326704.