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.
Inkinematics, thespeed (commonly referred to asv) of an object is themagnitude of the change of itsposition over time or the magnitude of the change of its position per unit of time; it is thus a non-negativescalar quantity.[1] Theaverage speed of an object in an interval of time is thedistance travelled by the object divided by theduration of the interval;[2] theinstantaneous speed is thelimit of the average speed as the duration of the time interval approaches zero. Speed is themagnitude ofvelocity (a vector), which indicates additionally the direction of motion.
Speed has thedimensions of distance divided by time. TheSI unit of speed is themetre per second (m/s), but the most common unit of speed in everyday usage is thekilometre per hour (km/h) or, in the US and the UK,miles per hour (mph). For air and marine travel, theknot is commonly used.
The fastest possible speed at which energy or information can travel, according tospecial relativity, is thespeed of light in vacuumc =299792458 metres per second (approximately1079000000 km/h or671000000 mph).Matter cannot quite reach the speed of light, as this would require an infinite amount of energy. In relativity physics, the concept ofrapidity replaces the classical idea of speed.
Definition
Historical definition
Italian physicistGalileo 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 iswhere is speed, is distance, and 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 avery short period of time, is calledinstantaneous speed. By looking at aspeedometer, 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 is defined as the magnitude of the instantaneousvelocity, that is, thederivative of the position with respect totime:[2][4]
If is the length of the path (also known as the distance) travelled until time, the speed equals the time derivative of:[2]
In the special case where the velocity is constant (that is, constant speed in a straight line), this can be simplified to.
Average speed
As an example, a bowling ball's speed when first released will be above its average speed, and after decelerating because of friction, its speed when reaching the pins will be below its 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
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, theslope of atangent line at any point of a distance-time graph is the instantaneous speed at this point, while the slope of achord line of the same graph is the average speed during the time interval covered by the chord.
Difference between speed and velocity
Speed denotes only how fast an object is moving, whereasvelocity describes both how fast and in which direction the object is moving.[5] If a car is said to travel at 60 km/h, itsspeed has been specified. However, if the car is said to move at 60 km/h to the north, itsvelocity has now been specified.
The big difference can be discerned when considering movement around acircle. When something moves in a circular path and returns to its starting point, its averagevelocity is zero, but its averagespeed is found by dividing thecircumference of the circle by the time taken to move around the circle. This is because the averagevelocity is calculated by considering only thedisplacement between the starting and end points, whereas the averagespeed considers only the totaldistance travelled.
Tangential speed (v) andangular speed (ω) on a spinning disc of radiusr.Tangential speed is the speed of an object undergoingcircular motion, i.e., moving along acircular path.[6] A point on the outside edge of amerry-go-round orturntable travels a greater distance in one completerotation 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 astangential speed because the direction of motion istangent to thecircumference of the circle. For circular motion, the terms linear speed and tangential speed are used interchangeably, and is measured inSI units as meters per second (m/s).
According toJean 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 byAlbert 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]
^"Origin of the speed/velocity terminology". History of Science and Mathematics Stack Exchange. Retrieved12 June 2023. Introduction of the speed/velocity terminology by Prof. Tait, in 1882.
^abcElert, Glenn."Speed & Velocity".The Physics Hypertextbook. Retrieved8 June 2017.
^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.
