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Question

If the time and displacement of particle along the positive X-axis are related as t=(x21)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 1x3
The relation between time and the displacement is given by the equation,
t=(x21)1/2
t2=x21. . . . . . . . . . .(1)
x2t2=1. . . .. . . . . . . .(2)
Differentiate equation (1) with respect to time,
2t=2xdxdt
Velocity, v=dxdt
2t=2xv
v=tx. . . . . . .(3)
Again differentiate the above equation,
2=2(xdx2dt2+dxdt.dxdt)
Acceleration, a=d2xdt2
1=xa+v2
xa=1v2
xa=1t2x2 (from equation 3)
xa=x2t2x2=1x2 (from equation 2)
Acceleration, a=1x3
The correct option is D.

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