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# Displacement,speed

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### Displacement,speed

1. 1. A displacement is the shortest distance from the initial to the final position of apoint P. Thus, it is the length of an imaginary straight path, typically distinctfrom the path actually travelled by P. A displacement vector represents thelength and direction of that imaginary straight path.A position vector expresses the position of a point P in space in terms of adisplacement from an arbitrary reference point O (typically the origin of a coordinatesystem). Namely, it indicates both the distance and direction of an imaginary motionalong a straight line from the reference position to the actual position of the point.A displacement may be also described as a relative position: the final position of apoint relative to its initial position and a displacement vector can be mathematicallydefined as the difference between the final and initial position vectors:
2. 2. In considering motions of objects over time the instantaneous velocity of theobject is the rate of change of the displacement as a function of time. Thevelocity then is distinct from the instantaneous speed which is the time rate ofchange of the distance traveled along a specific path. The velocity may beequivalently defined as the time rate of change of the position vector. If oneconsiders a moving initial position, or equivalently a moving origin (e.g. an initialposition or origin which is fixed to a train wagon, which in turn moves withrespect to its rail track), the velocity of P (e.g. a point representing the position ofa passenger walking on the train) may be referred to as a relative velocity, asopposed to an absolute velocity, which is computed with respect to a pointwhich is considered to be fixed in space (such as, for instance, a point fixed onthe floor of the train stationFor motion over a given interval of time, the displacement divided by the lengthof the time interval defines the average velocity.
3. 3. Rigid bodyIn dealing with the motion of a rigid body, the term displacement may alsoinclude the rotations of the body. In this case, the displacement of a particleof the body is called linear displacement(displacement along a line), while therotation of the body is called angular displacement.For a position vector s that is a function of time t, the derivatives can becomputed with respect to t. These derivatives have common utility in thestudy of kinematics, control theory, and other sciences and engineeringdisciplines.These common names correspond to terminology used in basickinematics. By extension, the higher order derivatives can be computed ina similar fashion. Study of these higher order derivatives can improveapproximations of the original displacement function. Such higher-orderterms are required in order to accurately represent the displacementfunction as a sum of an infinite series, enabling several analyticaltechniques in engineering and physics.
4. 4. DistanceDistance is a numerical description of how far apart objectsare. In physics or everyday discussion, distance may refer to aphysical length, or an estimation based on other criteria (e.g."two counties over"). In mathematics, a distance functionor metric is a generalization of the concept of physicaldistance. A metric is a function that behaves according to aspecific set of rules, and is a concrete way of describing whatit means for elements of some space to be "close to" or "faraway from" each other. In most cases, "distance from A to B" isinterchangeable with "distance between B and A".
5. 5. Distance is one of basic physical quantities hence it is "a property that can bequantified". Its basic SI unit is meter. Perhaps its not much of an answer, but itsas far you can go.Geometrically speaking, distance between two places is a function of theircoordinates or simply - just a number.Formula for the function that is used to calculate distance is called metric andcan be as simple as Pythagoras theorem in plane or very complicatedincorporating also time... (smart enough formula can describe how things falldown, it just needs to give smaller number (distance to the ground) for biggertime).
6. 6. Velocityvelocity is the rate of change of the position of an object, equivalent to aspecification of its speed and direction of motion. Speed describes only how fastan object is moving, whereas velocity gives both how fast and in what directionthe object is moving. If a car is said to travel at 60 km/h, its speed has beenspecified. However, if the car is said to move at 60 km/h to the north, its velocityhas now been specified. To have a constant velocity, an object must have aconstant speed in a constant direction. Constant direction constrains the objectto motion in a straight path (the objects path does not curve). Thus, a constantvelocity means motion in a straight line at a constant speed. If there is a changein speed, direction, or both, then the object is said to have a changing velocityand is undergoing an acceleration. For example, a car moving at a constant 20kilometers per hour in a circular path has a constant speed, but does not have aconstant velocity because its direction changes. Hence, the car is considered tobe undergoing an acceleration.
7. 7. Velocity is a vector physical quantity;both magnitude and direction arerequired to define it.The scalar absolute value (magnitude)of velocity is called "speed", a quantitythat is measured in meters persecond (m/s or m⋅s−1) when usingthe SI (metric) system. For example, "5meters per second" is a scalar (not avector), whereas "5 meters per secondeast" is a vector. The rate of change ofvelocity (in m/s) as a function of time(in s) is "acceleration" (in m/s2 – stated"meters per second per second"),which describes how an objects speedand direction of travel change at eachpoint in time. In science a"deceleration" is called a "negativeacceleration", for example: −2 m/s2.
8. 8. Speed is a scalar quantity in which direction of motion is unimportant(unlike the vector quantity velocity, in which both magnitude and directionmust be taken into consideration). Movement can be described by usingmotion graphs. Plotting distance against time in a distance–timegraph allows the total distance covered to be worked out. See also speed–time graph.Speed
9. 9. Different from instantaneous speed, average speed is defined as the total distancecovered over the time interval. For example, if a distance of 80 kilometers is driven in 1hour, the average speed is 80 kilometers per hour. Likewise, if 320 kilometers aretravelled in 4 hours, the average speed is also 80 kilometers per hour. When a distancein kilometers (km) is divided by a time in hours (h), the result is in kilometers per hour(km/h). Average speed does not describe the speed variations that may have takenplace during shorter time intervals (as it is the entire distance covered divided by thetotal time of travel), and so average speed is often quite different from a value ofinstantaneous speed. If the average speed and the time of travel are known, thedistance travelled can be calculated by rearranging the definition to
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