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.)

.

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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).