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Displacement

Blocks A and ...

Question

Blocks A and C start from rest and move to the right with acceleration and $a_{A} = 12 t m / s^{2} a n d a_{C} = 3 m / s^{2} .$ Here t is in seconds. The time when block B again comes to rest is $(g = 10 m / s^{2})$

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Solution

The correct option is D
From constraint relations, we can see that the acceleration of block B in upward direction is
$a_{B} = (\frac{a_{C} + a_{A}}{2})$ with proper signs.
So, $a_{B} = (\frac{3 - 12 t}{2}) = 1.5 - 6 t$
or $\frac{d v_{B}}{d t} = 1.5 - 6 t$
or $\int_{0}^{v_{B}} d v_{B} = \int_{0}^{1} (1.5 - 6 t) d t$
or $v_{B} = 1.5 t - 3 t^{2}$
or $v_{B} = 0 a t t = \frac{1}{2} s$

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