If the velocity of a moving particle , `v = prop x^n` where `x` is the displacement , then Options: A . &nbspwhen `x = 0` the velocity aand acceleration are zero B . &nbsp`n > 1/2` C . &nbsp`n D . &nbsp(A) and (B) are correct.

If the velocity of a m

Question -

If the velocity of a moving particle , `v = prop x^n` where `x` is the displacement , then

Options:

A . when `x = 0` the velocity aand acceleration are zero

B . `n > 1/2`

C . `n

D . (A) and (B) are correct.

Answer: Option D

Here `v prop x^n`

or `(dx)/(dt)= kx^n`

`:.` `(d^2 x)/(d t^2) = kn x^(n - 1) (dx)/(dt)`

or `(d^2x)/(d ^2) = knx^(n - 1) kx^n`

or ` (d^2 x)/(d t^2) = k^2 n x^(2n - 1)`

Since , at `x = o, v = 0`

It means fr moving the body , acceleration should be positive , for this.

`:.` `2n - 1 > 0`

`rArr n > 1/2`

If ` n < 1/2` particle remains in rest.

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