Q. 175.0( 3 Votes )

What is velocity-time graph? Sate how it can be used to find:

i. acceleration of a body

ii. the displacement of a body, and

iii. the distance travelled in a given time

Answer :

The Velocity – Time graph gives the change of velocity with the change in time.

Y – Axis : Velocity


X – Axis : Time


Now, slope of velocity – time graph is gives as


Slope = =


Since, y = v (Velocity)


And x = t (Time)


Now, there are three types of Velocity – Time graph.


a) Velocity is constant – Uniform Motion


This means that velocity remains same for all time.



b) Uniformly Accelerated Motion


This means that velocity changes at constant rate.


Slope = Constant and the graph is a straight line graph



c) Non – Uniformly Accelerated Motion


This means that velocity changes at a variable rate.


Slope = Variable and the graph is as shown below



Velocity – Time Graph can be used to find the following as:


a) Acceleration:


Slope of Velocity – Time Graph = Acceleration


Since, Slope =


So, Acceleration =


And hence, Slope = Acceleration


b) Displacement of a body:


The area under the velocity – time graph gives the displacement of the body.


Displacement = Velocity × Time


Area under the graph = Displacement of Body


For finding the area, we multiply the velocity and time.



c) Distance of a body:


Distance = Speed × Time


Now, Speed is magnitude of velocity.


Hence, as long as velocity is positive,


Area under the curve = Distance


NOTE:


If velocity is negative, then the area under the curve is negative and then the total area gives displacement. So, in that case,


Distance Displacement


Example:


Let the velocity – time graph be as shown below:



Now, Displacement = Area under the curve


=


= 5 m


Whereas, Distance =


= 15 m


For displacement we have considered the area below the time axis as negative whereas for distance, we have considered all areas as positive.


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