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Blocks A and ...

Question

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

A

2 s

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B

1 s

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C

3/2 s

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D

1/2 s

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Solution

The correct option is D
1/2 s

From constraint relations we can see that the acceleration of block B in upward direction is
$a_{B} = (\frac{a_{C} + a_{A}}{2}) w i t h p r o p e r s i g n s$
$S o a_{B} = (\frac{3 - 12 t}{2}) = 1.5 - 6 t$
$o r \frac{d v_{B}}{d t} = 1.5 - 6 t o r \int_{0}^{v_{B}} d v_{B} = t \int 0 (1.5 - 6 t) d t$
$o r v_{B} = 1.5 t - 3 t^{2} o r v_{B} = 0 a t t = \frac{1}{2} s$

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