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Velocity Vector
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector quantity, meaning that both magnitude and direction are needed to define it. The scalar absolute value ( magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an ''acceleration''. Definition Average velocity The average velocity of an object over a period of time is its change in position, \Delta s, divided by the duration of the period, \Delta t, given mathematically as\bar=\frac. Instantaneous velocity The instantaneous velocity of an object is the limit average velo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miles Per Hour
Miles per hour (mph, m.p.h., MPH, or mi/h) is a British imperial and United States customary unit of speed expressing the number of miles travelled in one hour. It is used in the United Kingdom, the United States, and a number of smaller countries, most of which are UK or US territories, or have close historical ties with the UK or US. Usage Road traffic Speed limits and road traffic speeds are given in miles per hour in the following jurisdictions: *Antigua and Barbuda *Bahamas *Belize *Dominica *Grenada *Liberia (occasionally) *Marshall Islands * Micronesia *Palau *Saint Kitts and Nevis *Saint Lucia * Saint Vincent and the Grenadines *United Kingdom *The following British Overseas Territories: **Anguilla **British Virgin Islands ** British Indian Ocean Territory **Cayman Islands **Falkland Islands **Montserrat **Saint Helena, Ascension and Tristan da Cunha **Turks and Caicos Islands *The Crown dependencies: **Bailiwick of Guernsey **Isle of Man **Jersey *United St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acceleration
In mechanics, acceleration is the Rate (mathematics), 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 Euclidean vector, vector quantities (in that they have Magnitude (mathematics), magnitude and Direction (geometry), direction). 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: * the net balance of all external forces acting onto that object — magnitude is Direct proportionality, directly proportional to this net resulting force; * that object's mass, depending on the materials out of which it is made — magnitude is Inverse proportionality, inversely proportional to the object's mass. The International System of Units, SI unit for acceleration is metre per second squared (, \ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Mean
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rate (mathematics), rates such as speeds, and is normally only used for positive arguments. The harmonic mean is the multiplicative inverse, reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, the generalized f-mean with f(x) = \frac. For example, the harmonic mean of 1, 4, and 4 is :\left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is :H(x_1, x_2, \ldots, x_n) = \frac = \frac. It is the reciprocal of the arithmetic mean of the reciprocals, and vice versa: :\begin H(x_1, x_2, \ldots, x_n) &= \frac, \\ A(x_1, x_2, \ldots, x_n) &= \frac, \end where the arithmetic mean is A(x_1, x_2, \ldots, x_n) = \tfrac1n \sum_^n x_i. The harmonic mean is a Schur-concave function, and is greater than or equal to the minimum of its arguments: for positive a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a Survey (statistics), survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps to distinguish it from other types of means, such as geometric mean, geometric and harmonic mean, harmonic. Arithmetic means are also frequently used in economics, anthropology, history, and almost every other academic field to some extent. For example, per capita income is the arithmetic average of the income of a nation's Human population, population. While the arithmetic mean is often used to report central tendency, central tendencies, it is not a robust statistic: it is greatly influenced by outliers (Value (mathematics), values much larger or smaller than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average Speed
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 non-negative scalar quantity. Introduction of the speed/velocity terminology by Prof. Tait, in 1882. 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; 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. 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 wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secant Line
In geometry, a secant is a line (geometry), line that intersects a curve at a minimum of two distinct Point (geometry), points.. The word ''secant'' comes from the Latin word ''secare'', meaning ''to cut''. In the case of a circle, a secant intersects the circle at exactly two points. A Chord (geometry), chord is the line segment determined by the two points, that is, the interval (mathematics), interval on the secant whose ends are the two points. Circles A straight line can intersect a circle at zero, one, or two points. A line with intersections at two points is called a ''secant line'', at one point a ''tangent line'' and at no points an ''exterior line''. A ''chord'' is the line segment that joins two distinct points of a circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord. In rigorous modern treatments of plane geometry, results that seem obvious and were assumed (without statement) by Euclid in Euclid's Elements, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. There are multiple different notations for differentiation. '' Leibniz notation'', named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas ''prime notation'' is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metre Per Second
The metre per second is the unit of both speed (a scalar (physics), scalar quantity) and velocity (a Vector (mathematics and physics), 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. According to the definition of metre, is exactly \frac of the speed of light. The International System of Units, SI unit symbols are m/s, m·s−1, m s−1, or . Conversions is equivalent to: : = 3.6 kilometres per hour, km/h (exactly) : ≈ 3.2808 feet per second (approximately) : ≈ 2.2369 miles per hour (approximately) : ≈ 1.9438 knot (unit), knots (approximately) 1 feet per second, foot per second = (exactly) 1 miles per hour, mile per hour = (exactly) 1 kilometres per hour, km/h = (exactly) Relation to other measures The benz, named in honour of Karl Benz, has been proposed as a name for one metre per second. Although it has seen some suppor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metre
The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of a second, where the second is defined by a hyperfine transition frequency of caesium. The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately . In 1799, the metre was redefined in terms of a prototype metre bar. The bar used was changed in 1889, and in 1960 the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length. From 1983 until 2019, the metre was formally defined as the length of the pat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar (mathematics)
A scalar is an element of a field which is used to define a ''vector space''. In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector. Generally speaking, a vector space may be defined by using any field instead of real numbers (such as complex numbers). Then scalars of that vector space will be elements of the associated field (such as complex numbers). A scalar product operation – not to be confused with scalar multiplication – may be defined on a vector space, allowing two vectors to be multiplied in the defined way to produce a scalar. A vector space equipped with a scalar product is called an inner product space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematics
In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with systems of specification of objects' positions and velocities and mathematical transformations between such systems. These systems may be rectangular like Cartesian coordinate system, cartesian, Curvilinear coordinates like polar coordinates or other systems. The object trajectories may be specified with respect to other objects which may themselve be in motion relative to a standard reference. Rotating systems may also be used. Numerous practical problems in kinematics involve constraints, such as mechanical linkages, ropes, or rolling disks. Overview Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, Physical object, bodies (objects), and systems of bodies (group ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being Derivative, differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given Function (mathematics), function between two points in the real line. Conventionally, areas above the horizontal Coordinate axis, axis of the plane are positive while areas below are n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
