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A point moves such that its displacement...

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

A

`2/x^5`

B

`(2t)/(x^5)`

C

`(2t)/(x^4)`

D

`(2t^2)/x^(5)`

Text Solution

Verified by Experts

The correct Answer is:
B
b. `x^3 = t^3+1 rArr 3x^2(dx)/(dt) = 3t^2 rArr (dx)/(dt) = t^2/x^2` ……….(i)
`(d^2x)/(dt^2) = (2tx^2-2x(dx)/(dt) t^2)/(x^4)`
`= 1/x^4 [ 2tx^2 - 2xt^2 t^2/x^2]`
`=(2tx^2)/x^4 [1-t^3/x^3]= (2tx^2)/x^4 [ 1-{(x^3-1)/x^3}] = (2t)/x^5`.
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