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Question

A point moves in a straight line so that its displacement x is given by x2=1+t2 where, x is in m and time t is in s. Its acceleration in m/s2 at time t is

A
tx3
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B
1x3
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C
x1x3
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D
t+1x3
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Solution

The correct option is B 1x3
Given, x2=1+t2
Differentiating the above equation we get
2xdx=2tdt xdxdt=t.........(i)
Now, taking differentiation of above equation for acceleration we get,
xd2xdt2+(dxdt)2=1
Or, xd2xdt2=1(tx)2
d2xdt2=x2t2x3=1x3 ( x2=1+t2 x2t2=1)
Hence, the acceleration is a=d2xdt2=1x3 m/s2


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