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. `3//2s`
D. `1//2s`

Answer

D

Explanation

From contraint relation we can see that acceleration
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)=1.5-6t`
or `underset(0)overset(v_(B))intdv_(B)=underset(0)overset(t)int(1.5-6t)dt orv_(B)=1.5t-3t^(2)`
or `v_(B)=0" at "t=1/2s`