Velocity - Time Graph

Physics

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Average velocity from velocity-time graph

Instantaneous velocity at a given time-instant for a particle can be found from the y-intercept of its velocity-time graph.
From a particle's velocity-time graph, its average velocity can be found by calculating the total area under the graph and then dividing it by the corresponding time-interval.
For a particle with uniform acceleration, velocity-time graph is a straight line. Its average velocity is given by . From the graph, this can be found by drawing the y-intercepts of initial and final velocities and then drawing the mid-point.
In the given graph, instantaneous velocity at and at .
Average velocity is found at E, i.e. mid-point of C and D.

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Acceleration from velocity-time graph

Acceleration of a particle is equal to the slope of a velocity-time graph.

In the given graph, 

Acceleration may be positive, negative or zero as it is a vector quantity. 

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Displacement from velocity-time graph

Displacement of a particle in a given time-interval is equal to the total area under the velocity-time graph in the given time-interval.
 In the given graph, displacement is found as area of trapezium ABCD.

Note: Since, displacement is a vector quantity, Area below the time-axis is considered as negative and above it is considered as positive. 

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Area under acceleration time graph

Change in velocity of a particle can be evaluated as area under the acceleration-time graph.

as
or
or (Which is area under the curve.)

diagram

Velocity Time graph for rest, uniform motion and uniform acceleration

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Velocity-time graph

The Velocity Time Graph: Velocity-time graph is a plot between Velocity and Time. It shows the Motion of the object that moves in a Straight Line. Magnitude of Velocity at a given instant is equal to its Instantaneous Speed. It is drawn for 1-D motion only and can take both positive and negative values.

In case where the acceleration is zero, tthe slope is zero ( horizontal line). If the acceleration is positive, then the slope is positive (an upward sloping line).

REVISE WITH CONCEPTS

Average Speed and Average Velocity

ExampleDefinitionsFormulaes

Instantaneous Velocity and Instantaneous Speed

ExampleDefinitionsFormulaes
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