Question

Blocks A and C start from rest and move to the right with acceleration $a_A=12tm{s}^{-2}and{a}_C=3m{s}^{-2}$. Here t is in seconds. The time when block B again comes to rest is

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

Answer 1

The correct option is D

1/2 s

From constraint relations we can see that the acceleration of block B in upward direction is
$a_B=(\frac{a_C+a_A}{2})withpropersigns$
$So{a}_B=(\frac{3-12t}{2})=1.5-6t$
$or\frac{d{v}_B}{dt}=1.5-6tor{\int }_0^{v_B}d{v}_B=\underset{0}{\overset{t}{\int }}(1.5-6t)dt$
$or{v}_B=1.5t-3t^{2}or{v}_B=0att=\frac{1}{2}s$