Block A and C start from rest and move to the right with acceleration `a_(A)=12t m//s^(2)` and `a_(C)=3m//s^(2)` Here t is in seconds. The time when block B attain comes to rest is:

Options

A. 2s
B. 1s
C. 2//2s
D. 1//4s

Explanation

From constraint relations , we can see that the acceleration of block B in upwart direction is
`a_(a)=((a_(c)+a_(A))/(2))` with proper signs.
So, `a_(a)=((3-12t)/(2))=1.5=6t`
(i) or `(dv_(B))/(dt)=1.5-6t`
(ii) or `underset(o)overset(v_(B))intdv_(B)=underset(o)overset(t)int(1.5-6t)dt`
or `v_(B)=1.5t-3t^(2)`
or `v_(B)=0.at t=(1\\2)s`