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Question

# In the one-dimensional motion of a particle, the relation between position x and time t is given by x2+2x=t , where x>0. Choose the correct statement.

A
The retardation of the particle is 14(x+1)3.
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B
The velocity of the particle is 1(x+1)3.
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C
Both are correct
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D
Both are wrong
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Solution

## The correct option is A The retardation of the particle is 14(x+1)3.Given, t=x2+2x (x>0) Differentiating with respect to ′x′ on both sides, dtdx=2x+2=2(x+1) v=dxdt=12(x+1) .....(1) Differentiating with respect to ′t′ on both sides, a=dvdt=−12(x+1)2.dxdt Using (1) in the above equation , we get a=−14(x+1)3 Hence, option (a) is the correct answer.

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