Block A and C starts from rest and move to the right with acceleration `a_(A)=12tms^(-2)` and `a_(C )=3ms^(-2)`. Here t is in second. The time when block B again comes to rest is

Options

A. `2s`
B. `1s`
C. `3//2s`
D. `1//2s`

Answer

D

Explanation

From constraint relation we can see that acceleration of block `B` is `a_(B)=((a_(A)+a_(C))/(2))` with proper signs. Hence `a_(B)=((3-12t)/(2))=1.5-6t or`
`(dv_(B))/(dt)=1.5-6 orunderset(0)overset(v_(B))intdv_(B)=underset(0)overset(t)int(1.5-6t)dt` or
`v_(B) = 1.5t -3t^(2)` or `v_(B) =0` at `= (1)/(2)s` .