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//2 s`
D. `1//2 s`

Answer

D

Explanation

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