As shown in the figure, initially both th springs are in normal length `(L_(0))`. At t=0, the block is given a rightward velocity `v_(0)=2 m//s`. The mass of the block is `(14//3)kg`. How much distance does th block cover before it comes to rest for the first time? (The spring constant of the left spring is `K_(0)=2N//m` and that of the right spring is not constant and varies as `k=k_(0)x`, where x is the compression in the spring)

Options

A. 2m
B. 4m
C. 6m
D. 8m

Answer

A

Explanation

`(1)/(2)mv_(0)^(2)=(1)/(2)K_(0)((2)/(3)x^(2)+x^(2))`
`rArr(1)/(2)((14)/(3))(2)^(2)=(1)/(2)xx2xx((2)/(3)x^(3)+x^(2))`
`rArr 2x^(3)+3x^(2)-28=0`
`rArr2x^(2)(x-2)+7x(x-2)+14(x-2)=0`
`rArrx=2m`