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Question

Velocity versus displacement graph of a particle moving in a straight line is as shown in figure. The acceleration of the particle is:

A
Increases linearly with x
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B
Constant
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C
Increases parabolically with x
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D
None
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Solution

The correct option is A Increases linearly with x

From the graph, velocity-displacement equation can be written as:
v=vo+αx(1)
Here, vo and α are positive constants.
Differentiating Eq. (1) with respect to x we get, dvdx=α=constant
Acceleration of the particle can be written as
a=dvdt
Or, a=vdvdx
a=(vo+αx)α=v0α+α2x
Above equation signifies linear relationship of a and x. Thus, acceleration increases linearly with x.

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