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Question

For a particle moving along x - axis, the acceleration a of the particle in terms of its x - coordinate x is given by a=9x, where x is in meters and a is in m/s2. Take acceleration, velocity and displacement in positive x - direction as positive. The initial velocity of particle at x=0 is u=+6 m/s. The plot of velocity versus x - coordinate of particle in the duration it moves from origin towards the positive x - direction, is best represented by

A
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B
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C
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D
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Solution

The correct option is D
Given a=9x
We know that, a=dvdt=vdvdx
vdvdx=9x
v dv=9x dx
On integrating both sides, we get
v22=9x22+C
At x=0,v=u=+6 m/s
C=18
v22=9x22+18 ......(i)
In this relation v is not varying linearly with , therefore graphs (a), (b) and (c) are incorrect.
Equation (i) implies quadratic relation between v and x.
Hence, the correct answer is option (d).

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