Question

# If the time and displacement of particle along the positive X-axis are related as t=(x2âˆ’1)12, then find the acceleration in terms of x.

A
1x4
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B
1x7
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C
1x
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D
1x3
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Solution

## The correct option is C 1x3The relation between time and the displacement is given by the equation,t=(x2−1)1/2t2=x2−1. . . . . . . . . . .(1)x2−t2=1. . . .. . . . . . . .(2)Differentiate equation (1) with respect to time,2t=2xdxdtVelocity, v=dxdt2t=2xv v=tx. . . . . . .(3)Again differentiate the above equation,2=2(xdx2dt2+dxdt.dxdt)Acceleration, a=d2xdt21=xa+v2 xa=1−v2xa=1−t2x2 (from equation 3)xa=x2−t2x2=1x2 (from equation 2)Acceleration, a=1x3The correct option is D.

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