First slide
Rectilinear Motion

The distance x covered by a body moving in a straight line in time t is given by the relation 2x2+3x=t. If v is the velocity of the body at a certain instant of time, its acceleration will be


Differentiating 2x2+3x=t with respect to t we have 4xdxdt+3dxdt=1   …….(i)

Now dxdt=v. Therefore, 4xv+3v=1 or 4x+3=1/v. Differentiating Eq. (i) with respect to time t, we have 4dxdt2+4xd2xdt2+3d2xdt2=0

or  4v2+4xa+3a=0

or  a=4v24x+3  ………(ii)

where a=d2xdt2 is the acceleration. But 4x+3=1/v. Using this in Eq. (ii) we get a=4v3. Hence the correct choice is (d).

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