About: Motion graphs and derivatives

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In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units, the position of the moving object is measured in meters relative to the origin, while the time is measured in seconds. Placing position on the y-axis and time on the x-axis, the slope of the curve is given by: The same multiplication rule holds true for acceleration vs. time graphs. When acceleration is multiplied

Attributes	Values
rdfs:label	Motion graphs and derivatives (en)
rdfs:comment	In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units, the position of the moving object is measured in meters relative to the origin, while the time is measured in seconds. Placing position on the y-axis and time on the x-axis, the slope of the curve is given by: The same multiplication rule holds true for acceleration vs. time graphs. When acceleration is multiplied (en)
foaf:depiction
dct:subject	Classical mechanics
Wikipage page ID	3391482 (xsd:integer)
Wikipage revision ID	1030208200 (xsd:integer)
Link from a Wikipage to another Wikipage	Derivative Velocity Second Mechanics Origin (mathematics) Arithmetic mean Slope Time Acceleration Addison-Wesley Graph of a function Definite integral Kinematics Classical mechanics Displacement (vector) Position (vector) Infinitesimal Integral Metre per second squared Reading, Massachusetts Second derivative Linear SI X-axis Y-axis
sameAs	Motion graphs and derivatives Motion graphs and derivatives Motion graphs and derivatives
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Kinematics
thumbnail	wiki-commons:Special:FilePath/Acceleration.svg?width=300
has abstract	In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units, the position of the moving object is measured in meters relative to the origin, while the time is measured in seconds. Placing position on the y-axis and time on the x-axis, the slope of the curve is given by: Here is the position of the object, and is the time. Therefore, the slope of the curve gives the change in position divided by the change in time, which is the definition of the average velocity for that interval of time on the graph. If this interval is made to be infinitesimally small, such that becomes and becomes , the result is the instantaneous velocity at time , or the derivative of the position with respect to time. A similar fact also holds true for the velocity vs. time graph. The slope of a velocity vs. time graph is acceleration, this time, placing velocity on the y-axis and time on the x-axis. Again the slope of a line is change in over change in : where is the velocity, and is the time. This slope therefore defines the average acceleration over the interval, and reducing the interval infinitesimally gives , the instantaneous acceleration at time , or the derivative of the velocity with respect to time (or the second derivative of the position with respect to time). In SI, this slope or derivative is expressed in the units of meters per second per second . Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.) The same multiplication rule holds true for acceleration vs. time graphs. When acceleration is multiplied (en)
prov:wasDerivedFrom	wikipedia-en:Motion_graphs_and_derivatives?oldid=1030208200&ns=0
page length (characters) of wiki page	5004 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Motion_graphs_and_derivatives
is Link from a Wikipage to another Wikipage of	Index of physics articles (M) List of physics concepts in primary and secondary education curricula Linear motion D-t graph Time derivative Displacement vs. time graph V-t graph Velocity vs. time graph Position vs. time curves Position vs. time graph
is Wikipage redirect of	D-t graph Displacement vs. time graph V-t graph Velocity vs. time graph Position vs. time curves Position vs. time graph
is foaf:primaryTopic of	wikipedia-en:Motion_graphs_and_derivatives

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