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 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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Important Questions

A car moves with a speed of 40 km/h for 15 minutes and then with a speed of 60 km/h for the next 15 minutes. The total distance covered by the car is : 

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A man walks on a straight road from his home to a market  away with a speed of . Finding the market closed, he instantly turns and walks back home with a speed of . What is the
(a) magnitude of average velocity, and
(b) average speed of the man over the interval of time
(i)  to ,
(ii)  to  
(iii)  to

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The position of an object moving along x-axis is given by x = a + , where a = 8.5 m and b = 2.5 m and t is measured in seconds. The average velocity of the object between t = 2 s and t = 4 s is

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A car travels from A to B at a, speed of and returns at a speed of . The average speed of the car for the whole journey is:

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A car travels the first one third of a certain distance with a speed of 10 km/hr, the next one third with a speed of 20 km/hr and the last one third distance with a speed of 60 km/hr The average speed of the car for the whole journey is

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A car covers the first half the distance  between two places at 40 km/h another half at 60 km/h, the average speed of car

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An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth.

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A particle moving in a straight line covers half the distance with speed of . The other half of the distance is covered in two equal time interval with speed of and respectively. The average speed of the particle during this motion is 

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Joseph Jogs from one end  to the other end  of a straight  road in  minutes  seconds and then turns around and jogs  back to point  in another  minute. What are Joseph's average speeds and velocities in jogging (a) from  to  and (b) from  to ?

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A motorcyclist drives from A to B with a uniform speed of and returns with a speed of . Find the average speed.

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