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Question

A point moves in a straight line so that its displacement x at time t is given by equation x2=t2+1. Its acceleration is:

A
1x
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B
1x3
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C
1x2
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D
1x3
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Solution

The correct option is B 1x3
Differentiating w.r.t t on both sides,
2xdxdt=2t+0
xv=tv=tx
Differentiating again w.r.t t,
xdvdt+vdxdt=1
xa+v2=1
xa=1v2
xa=1t2x2 (xv=t)
xa=1[x21x2] (x2=t2+1)
xa=11+1x2
a=1x3

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