59-571: General James M. Gavin Power Plant is a 2,600- megawatt supercritical coal-fired power station in the village of Cheshire, Ohio , United States. It is owned by Lightstone Generation LLC, a 50–50 joint venture of The Blackstone Group L.P. and ArcLight Capital Partners. Gavin is the largest coal-fired power facility in Ohio, and one of the largest in the US, capable of powering two million homes. In February 2017,
118-491: A ⋅ x ) {\displaystyle \therefore v^{2}=u^{2}+2({\boldsymbol {a}}\cdot {\boldsymbol {x}})} where v = | v | etc. The above equations are valid for both Newtonian mechanics and special relativity . Where Newtonian mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in Newtonian mechanics, all observers agree on
177-605: A ) ⋅ x = ( 2 a ) ⋅ ( u t + 1 2 a t 2 ) = 2 t ( a ⋅ u ) + a 2 t 2 = v 2 − u 2 {\displaystyle (2{\boldsymbol {a}})\cdot {\boldsymbol {x}}=(2{\boldsymbol {a}})\cdot ({\boldsymbol {u}}t+{\tfrac {1}{2}}{\boldsymbol {a}}t^{2})=2t({\boldsymbol {a}}\cdot {\boldsymbol {u}})+a^{2}t^{2}=v^{2}-u^{2}} ∴ v 2 = u 2 + 2 (
236-447: A = d v d t . {\displaystyle {\boldsymbol {a}}={\frac {d{\boldsymbol {v}}}{dt}}.} From there, velocity is expressed as the area under an a ( t ) acceleration vs. time graph. As above, this is done using the concept of the integral: v = ∫ a d t . {\displaystyle {\boldsymbol {v}}=\int {\boldsymbol {a}}\ dt.} In
295-546: A light bulb with a power rating of 100 W is turned on for one hour, the energy used is 100 watt hours (W·h), 0.1 kilowatt hour, or 360 kJ . This same amount of energy would light a 40-watt bulb for 2.5 hours, or a 50-watt bulb for 2 hours. Power stations are rated using units of power, typically megawatts or gigawatts (for example, the Three Gorges Dam in China is rated at approximately 22 gigawatts). This reflects
354-417: A constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Hence, the car is considered to be undergoing an acceleration. Since the derivative of the position with respect to time gives the change in position (in metres ) divided by the change in time (in seconds ), velocity is measured in metres per second (m/s). Velocity
413-556: A part of a $ 2.17 billion deal in 2016. The power plant has been using unlined pits to store its fly ash , which could contaminate groundwater . The facility's owners applied for a permit from the United States Environmental Protection Agency (EPA) to continue operating and using the unlined pits. In November 2022, the EPA ordered the utility to stop dumping coal ash into unlined storage ponds and speed cleanup of
472-411: A period of one year: equivalent to approximately 114 megawatts of constant power output. The watt-second is a unit of energy, equal to the joule . One kilowatt hour is 3,600,000 watt seconds. While a watt per hour is a unit of rate of change of power with time, it is not correct to refer to a watt (or watt-hour) as a watt per hour. Velocity Velocity is the speed in combination with
531-535: A turbine, which generates 648 MW e (i.e. electricity). Other SI prefixes are sometimes used, for example gigawatt electrical (GW e ). The International Bureau of Weights and Measures , which maintains the SI-standard, states that further information about a quantity should not be attached to the unit symbol but instead to the quantity symbol (e.g., P th = 270 W rather than P = 270 W th ) and so these unit symbols are non-SI. In compliance with SI,
590-588: A two-dimensional system, where there is an x-axis and a y-axis, corresponding velocity components are defined as v x = d x / d t , {\displaystyle v_{x}=dx/dt,} v y = d y / d t . {\displaystyle v_{y}=dy/dt.} The two-dimensional velocity vector is then defined as v =< v x , v y > {\displaystyle {\textbf {v}}=<v_{x},v_{y}>} . The magnitude of this vector represents speed and
649-486: A unit of time, namely 1 J/s. In this new definition, 1 absolute watt = 1.00019 international watts. Texts written before 1948 are likely to be using the international watt, which implies caution when comparing numerical values from this period with the post-1948 watt. In 1960, the 11th General Conference on Weights and Measures adopted the absolute watt into the International System of Units (SI) as
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#1732858988125708-402: A velocity vector, denotes only how fast an object is moving, while velocity indicates both an object's speed and direction. To have a constant velocity , an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed. For example, a car moving at
767-441: Is a stub . You can help Misplaced Pages by expanding it . Megawatt The watt (symbol: W ) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m ⋅s . It is used to quantify the rate of energy transfer . The watt is named in honor of James Watt (1736–1819), an 18th-century Scottish inventor , mechanical engineer , and chemist who improved
826-468: Is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. The drag force, F D {\displaystyle F_{D}} , is dependent on the square of velocity and is given as F D = 1 2 ρ v 2 C D A {\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A} where Escape velocity
885-417: Is always less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, displacement can increase or decrease in magnitude as well as change direction. In terms of a displacement-time ( x vs. t ) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the slope of the tangent line to the curve at any point , and
944-504: Is connected to the electric transmission grid by 765-kilovolt transmission lines. In 2002, to avoid lawsuits relating to air pollution in the village of Cheshire, the American Electric Power (AEP) corporation decided to buy out the town, by paying every homeowner 3.5 times the market value of their home to move. The total deal came to around $ 20 million. AEP sold Gavin along with three other plants to Blackstone and ArcLight as
1003-720: Is defined as v =< v x , v y , v z > {\displaystyle {\textbf {v}}=<v_{x},v_{y},v_{z}>} with its magnitude also representing speed and being determined by | v | = v x 2 + v y 2 + v z 2 . {\displaystyle |v|={\sqrt {v_{x}^{2}+v_{y}^{2}+v_{z}^{2}}}.} While some textbooks use subscript notation to define Cartesian components of velocity, others use u {\displaystyle u} , v {\displaystyle v} , and w {\displaystyle w} for
1062-501: Is defined as the rate of change of position with respect to time, which may also be referred to as the instantaneous velocity to emphasize the distinction from the average velocity. In some applications the average velocity of an object might be needed, that is to say, the constant velocity that would provide the same resultant displacement as a variable velocity in the same time interval, v ( t ) , over some time period Δ t . Average velocity can be calculated as: The average velocity
1121-435: Is defined as the rate of change of position, it is often common to start with an expression for an object's acceleration . As seen by the three green tangent lines in the figure, an object's instantaneous acceleration at a point in time is the slope of the line tangent to the curve of a v ( t ) graph at that point. In other words, instantaneous acceleration is defined as the derivative of velocity with respect to time:
1180-483: Is found by the distance formula as | v | = v x 2 + v y 2 . {\displaystyle |v|={\sqrt {v_{x}^{2}+v_{y}^{2}}}.} In three-dimensional systems where there is an additional z-axis, the corresponding velocity component is defined as v z = d z / d t . {\displaystyle v_{z}=dz/dt.} The three-dimensional velocity vector
1239-635: Is given by the harmonic mean of the speeds v ¯ = n ( 1 v 1 + 1 v 2 + 1 v 3 + ⋯ + 1 v n ) − 1 = n ( ∑ i = 1 n 1 v i ) − 1 . {\displaystyle {\bar {v}}=n\left({1 \over v_{1}}+{1 \over v_{2}}+{1 \over v_{3}}+\dots +{1 \over v_{n}}\right)^{-1}=n\left(\sum _{i=1}^{n}{\frac {1}{v_{i}}}\right)^{-1}.} Although velocity
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#17328589881251298-700: Is named after the Scottish inventor James Watt . The unit name was proposed by C. William Siemens in August 1882 in his President's Address to the Fifty-Second Congress of the British Association for the Advancement of Science . Noting that units in the practical system of units were named after leading physicists, Siemens proposed that watt might be an appropriate name for a unit of power. Siemens defined
1357-474: Is position and r ^ {\displaystyle {\hat {\boldsymbol {r}}}} is the radial direction. The transverse speed (or magnitude of the transverse velocity) is the magnitude of the cross product of the unit vector in the radial direction and the velocity vector. It is also the dot product of velocity and transverse direction, or the product of the angular speed ω {\displaystyle \omega } and
1416-409: Is the gravitational constant and g is the gravitational acceleration . The escape velocity from Earth's surface is about 11 200 m/s, and is irrespective of the direction of the object. This makes "escape velocity" somewhat of a misnomer, as the more correct term would be "escape speed": any object attaining a velocity of that magnitude, irrespective of atmosphere, will leave the vicinity of
1475-769: Is the component of velocity along a circle centered at the origin. v = v T + v R {\displaystyle {\boldsymbol {v}}={\boldsymbol {v}}_{T}+{\boldsymbol {v}}_{R}} where The radial speed (or magnitude of the radial velocity) is the dot product of the velocity vector and the unit vector in the radial direction. v R = v ⋅ r | r | = v ⋅ r ^ {\displaystyle v_{R}={\frac {{\boldsymbol {v}}\cdot {\boldsymbol {r}}}{\left|{\boldsymbol {r}}\right|}}={\boldsymbol {v}}\cdot {\hat {\boldsymbol {r}}}} where r {\displaystyle {\boldsymbol {r}}}
1534-418: Is the mass of the object. The kinetic energy of a moving object is dependent on its velocity and is given by the equation E k = 1 2 m v 2 {\displaystyle E_{\text{k}}={\tfrac {1}{2}}mv^{2}} where E k is the kinetic energy. Kinetic energy is a scalar quantity as it depends on the square of the velocity. In fluid dynamics , drag
1593-461: Is the mass times the distance to the origin times the transverse velocity, or equivalently, the mass times the distance squared times the angular speed. The sign convention for angular momentum is the same as that for angular velocity. L = m r v T = m r 2 ω {\displaystyle L=mrv_{T}=mr^{2}\omega } where The expression m r 2 {\displaystyle mr^{2}}
1652-547: Is the minimum speed a ballistic object needs to escape from a massive body such as Earth. It represents the kinetic energy that, when added to the object's gravitational potential energy (which is always negative), is equal to zero. The general formula for the escape velocity of an object at a distance r from the center of a planet with mass M is v e = 2 G M r = 2 g r , {\displaystyle v_{\text{e}}={\sqrt {\frac {2GM}{r}}}={\sqrt {2gr}},} where G
1711-523: Is the rate at which electrical work is performed when a current of one ampere (A) flows across an electrical potential difference of one volt (V), meaning the watt is equivalent to the volt-ampere (the latter unit, however, is used for a different quantity from the real power of an electrical circuit). 1 W = 1 V ⋅ A . {\displaystyle \mathrm {1~W=1~V{\cdot }A} .} Two additional unit conversions for watt can be found using
1770-458: Is the rate of rotation about the origin (with positive quantities representing counter-clockwise rotation and negative quantities representing clockwise rotation, in a right-handed coordinate system). The radial and traverse velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components. The transverse velocity
1829-453: Is the speed of light. Relative velocity is a measurement of velocity between two objects as determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles. Consider an object A moving with velocity vector v and an object B with velocity vector w ; these absolute velocities are typically expressed in
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1888-436: The x {\displaystyle x} -, y {\displaystyle y} -, and z {\displaystyle z} -axes respectively. In polar coordinates , a two-dimensional velocity is described by a radial velocity , defined as the component of velocity away from or toward the origin, and a transverse velocity , perpendicular to the radial one. Both arise from angular velocity , which
1947-811: The Newcomen engine with his own steam engine in 1776. Watt's invention was fundamental for the Industrial Revolution . When an object's velocity is held constant at one meter per second against a constant opposing force of one newton , the rate at which work is done is one watt. 1 W = 1 J / s = 1 N ⋅ m / s = 1 k g ⋅ m 2 ⋅ s − 3 . {\displaystyle \mathrm {1~W=1~J{/}s=1~N{\cdot }m{/}s=1~kg{\cdot }m^{2}{\cdot }s^{-3}} .} In terms of electromagnetism , one watt
2006-483: The SI ( metric system ) as metres per second (m/s or m⋅s ). 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 . The average velocity of an object over a period of time is its change in position , Δ s {\displaystyle \Delta s} , divided by
2065-424: The derivative of the position with respect to time: v = lim Δ t → 0 Δ s Δ t = d s d t . {\displaystyle {\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {s}}}{\Delta t}}={\frac {d{\boldsymbol {s}}}{dt}}.} From this derivative equation, in
2124-423: The above equation and Ohm's law . 1 W = 1 V 2 / Ω = 1 A 2 ⋅ Ω , {\displaystyle \mathrm {1~W=1~V^{2}/\Omega =1~A^{2}{\cdot }\Omega } ,} where ohm ( Ω {\displaystyle \Omega } ) is the SI derived unit of electrical resistance . The watt
2183-1574: The average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity. If t 1 = t 2 = t 3 = ... = t , then average speed is given by the arithmetic mean of the speeds v ¯ = v 1 + v 2 + v 3 + ⋯ + v n n = 1 n ∑ i = 1 n v i {\displaystyle {\bar {v}}={v_{1}+v_{2}+v_{3}+\dots +v_{n} \over n}={\frac {1}{n}}\sum _{i=1}^{n}{v_{i}}} v ¯ = s 1 + s 2 + s 3 + ⋯ + s n t 1 + t 2 + t 3 + ⋯ + t n = s 1 + s 2 + s 3 + ⋯ + s n s 1 v 1 + s 2 v 2 + s 3 v 3 + ⋯ + s n v n {\displaystyle {\bar {v}}={s_{1}+s_{2}+s_{3}+\dots +s_{n} \over t_{1}+t_{2}+t_{3}+\dots +t_{n}}={{s_{1}+s_{2}+s_{3}+\dots +s_{n}} \over {{s_{1} \over v_{1}}+{s_{2} \over v_{2}}+{s_{3} \over v_{3}}+\dots +{s_{n} \over v_{n}}}}} If s 1 = s 2 = s 3 = ... = s , then average speed
2242-451: The base body as long as it does not intersect with something in its path. In special relativity , the dimensionless Lorentz factor appears frequently, and is given by γ = 1 1 − v 2 c 2 {\displaystyle \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}} where γ is the Lorentz factor and c
2301-402: The concept of an instantaneous velocity might at first seem counter-intuitive, it may be thought of as the velocity that the object would continue to travel at if it stopped accelerating at that moment. While the terms speed and velocity are often colloquially used interchangeably to connote how fast an object is moving, in scientific terms they are different. Speed, the scalar magnitude of
2360-462: The controls reduce mercury emissions by up to 91% and particulates by 99%. The plant contributes approximately $ 6 million a year in property taxes that support the Gallia County school system and government. The plant is Gallia County's largest taxpayer and makes annual contributions of more than $ 50,000 to local charities and non-profits. This article about a United States power station
2419-402: 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. Velocity is a physical vector quantity : both magnitude and direction are needed to define it. The scalar absolute value ( magnitude ) of velocity is called speed , being a coherent derived unit whose quantity is measured in
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2478-458: The duration of the period, Δ t {\displaystyle \Delta t} , given mathematically as v ¯ = Δ s Δ t . {\displaystyle {\bar {v}}={\frac {\Delta s}{\Delta t}}.} The instantaneous velocity of an object is the limit average velocity as the time interval approaches zero. At any particular time t , it can be calculated as
2537-515: The energy company Ørsted A/S uses the unit megawatt for produced electrical power and the equivalent unit megajoule per second for delivered heating power in a combined heat and power station such as Avedøre Power Station . When describing alternating current (AC) electricity, another distinction is made between the watt and the volt-ampere . While these units are equivalent for simple resistive circuits , they differ when loads exhibit electrical reactance . Radio stations usually report
2596-540: The inertial frame chosen is that in which the latter of the two mentioned objects is in rest. In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with special relativity in which velocities depend on the choice of reference frame. In the one-dimensional case, the velocities are scalars and the equation is either: v rel = v − ( − w ) , {\displaystyle v_{\text{rel}}=v-(-w),} if
2655-460: The maximum power output it can achieve at any point in time. A power station's annual energy output, however, would be recorded using units of energy (not power), typically gigawatt hours. Major energy production or consumption is often expressed as terawatt hours for a given period; often a calendar year or financial year. One terawatt hour of energy is equal to a sustained power delivery of one terawatt for one hour, or approximately 114 megawatts for
2714-477: The one-dimensional case it can be seen that the area under a velocity vs. time ( v vs. t graph) is the displacement, s . In calculus terms, the integral of the velocity function v ( t ) is the displacement function s ( t ) . In the figure, this corresponds to the yellow area under the curve. s = ∫ v d t . {\displaystyle {\boldsymbol {s}}=\int {\boldsymbol {v}}\ dt.} Although
2773-493: The plant represented slightly more than 11% of the total electric generation capacity in Ohio according to the Energy Information Administration (EIA). The plant was named in honor of James Maurice "Jumpin' Jim" Gavin , the third Commanding General (CG) of the 82nd Airborne Division during World War II . Gavin's two units, rated at 1,300 MW each, were placed into service in 1974 and 1975. The power plant
2832-488: The power of their transmitters in units of watts, referring to the effective radiated power . This refers to the power that a half-wave dipole antenna would need to radiate to match the intensity of the transmitter's main lobe . The terms power and energy are closely related but distinct physical quantities. Power is the rate at which energy is generated or consumed and hence is measured in units (e.g. watts) that represent energy per unit time . For example, when
2891-754: The radius (the magnitude of the position). v T = | r × v | | r | = v ⋅ t ^ = ω | r | {\displaystyle v_{T}={\frac {|{\boldsymbol {r}}\times {\boldsymbol {v}}|}{|{\boldsymbol {r}}|}}={\boldsymbol {v}}\cdot {\hat {\boldsymbol {t}}}=\omega |{\boldsymbol {r}}|} such that ω = | r × v | | r | 2 . {\displaystyle \omega ={\frac {|{\boldsymbol {r}}\times {\boldsymbol {v}}|}{|{\boldsymbol {r}}|^{2}}}.} Angular momentum in scalar form
2950-710: The same inertial reference frame . Then, the velocity of object A relative to object B is defined as the difference of the two velocity vectors: v A relative to B = v − w {\displaystyle {\boldsymbol {v}}_{A{\text{ relative to }}B}={\boldsymbol {v}}-{\boldsymbol {w}}} Similarly, the relative velocity of object B moving with velocity w , relative to object A moving with velocity v is: v B relative to A = w − v {\displaystyle {\boldsymbol {v}}_{B{\text{ relative to }}A}={\boldsymbol {w}}-{\boldsymbol {v}}} Usually,
3009-698: The site. The plant may have to pause or even cease operations in order to comply with the order. The order becomes effective 135 days after publication in the Federal Register. If additional time is needed, the order included a process to address demonstrated grid reliability issues. Gavin is equipped with a suite of air quality controls. These include selective catalytic reduction units that reduce nitrogen oxide ( NO x ) emissions by 82%; flue-gas desulfurization (FGD) units (scrubbers) that remove 94% of sulfur dioxide ( SO 2 ) emissions and electrostatic precipitators for particulate control. Together
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#17328589881253068-432: The special case of constant acceleration, velocity can be studied using the suvat equations . By considering a as being equal to some arbitrary constant vector, this shows v = u + a t {\displaystyle {\boldsymbol {v}}={\boldsymbol {u}}+{\boldsymbol {a}}t} with v as the velocity at time t and u as the velocity at time t = 0 . By combining this equation with
3127-415: The suvat equation x = u t + a t /2 , it is possible to relate the displacement and the average velocity by x = ( u + v ) 2 t = v ¯ t . {\displaystyle {\boldsymbol {x}}={\frac {({\boldsymbol {u}}+{\boldsymbol {v}})}{2}}t={\boldsymbol {\bar {v}}}t.} It is also possible to derive an expression for
3186-401: The two objects are moving in opposite directions, or: v rel = v − ( + w ) , {\displaystyle v_{\text{rel}}=v-(+w),} if the two objects are moving in the same direction. In multi-dimensional Cartesian coordinate systems , velocity is broken up into components that correspond with each dimensional axis of the coordinate system. In
3245-559: The unit of power. In the electric power industry , megawatt electrical ( MWe or MW e ) refers by convention to the electric power produced by a generator, while megawatt thermal or thermal megawatt (MWt, MW t , or MWth, MW th ) refers to thermal power produced by the plant. For example, the Embalse nuclear power plant in Argentina uses a fission reactor to generate 2,109 MW t (i.e. heat), which creates steam to drive
3304-556: The unit within the existing system of practical units as "the power conveyed by a current of an Ampère through the difference of potential of a Volt". In October 1908, at the International Conference on Electric Units and Standards in London, so-called international definitions were established for practical electrical units. Siemens' definition was adopted as the international watt. (Also used: 1 A × 1 Ω.) The watt
3363-555: The value of t and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. In other words, only relative velocity can be calculated. In classical mechanics, Newton's second law defines momentum , p, as a vector that is the product of an object's mass and velocity, given mathematically as p = m v {\displaystyle {\boldsymbol {p}}=m{\boldsymbol {v}}} where m
3422-648: The velocity independent of time, known as the Torricelli equation , as follows: v 2 = v ⋅ v = ( u + a t ) ⋅ ( u + a t ) = u 2 + 2 t ( a ⋅ u ) + a 2 t 2 {\displaystyle v^{2}={\boldsymbol {v}}\cdot {\boldsymbol {v}}=({\boldsymbol {u}}+{\boldsymbol {a}}t)\cdot ({\boldsymbol {u}}+{\boldsymbol {a}}t)=u^{2}+2t({\boldsymbol {a}}\cdot {\boldsymbol {u}})+a^{2}t^{2}} ( 2
3481-420: Was defined as equal to 10 units of power in the practical system of units. The "international units" were dominant from 1909 until 1948. After the 9th General Conference on Weights and Measures in 1948, the international watt was redefined from practical units to absolute units (i.e., using only length, mass, and time). Concretely, this meant that 1 watt was defined as the quantity of energy transferred in
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