A point moves such that its displacement as a function of time is given by `x^3 = t^3 + 1`. Its acceleration as a function of time t will be

Options

A. `(2)/(x^(5))`
B. `(2t)/(x^(5))`
C. `(2t)/(x^(4))`
D. `(2t^(2))/(x^(5))`

Explanation

`x^(2)=t^(3)+1 rArr 3x^(2)(dx)/(dt)=3t^(2)`
`x^(2)v=t^(2) rArr 2x(dx)/(dt)v+x^(2)a=2t`
`2x(t^(4))/(x^(4))+x^(2)a=2trArr x^(2)a=2t-(2t^(4))/(x^(3))`
`a=(2t[x^(3)-t^(3)])/(x^(5))rArr a-(2t)/(x^(5))`