In the given find the and acceleration of `B` if instantaneous velocity and acceleration of `A` are as shown in the
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Answer

1

Explanation

We use the fact that string is inextensible and length of string is constant `l_(1) +l_(2) + l_(3) +l_(4)=` constant differentiate to get
`(dl_(1))/(dt) + (dl_(2))/(dt) +(dl_(3))/(dt)+(dl_(4))/(dt)=0`
`v_(A)+v_(A)(-v_(C))+(-v_(C))=0`
or `v_(C) =v_(A) rArr v_(C) = 1m//suarr`
where `v_(c)` is velocity of pulley `C`
Similarly `a_(C) =a_(A)`
`:. a_(C) =2m//s^(2) darr`
Now `l_(4) +l_(5) =l_(6)`
`:. (dl_(4))/(dt) + (dl_(5))/(dt) = (dl_(6))/(dt)`
`:. -v_(C)+(v_(B)) =-v_(B)`
`:. v_(B) = 0.5 m//suarr`
Similarly, `a_(B) = (a_(C))/(2) :. a_(B) = 1m//s^(2)darr`
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