Block B has a downward velocity in `m//s` and given by `v_(B)=t^(2)/2+t^(3)/6`, where t is in s. Acceleration of A at `t=2` second is

Options

A. `2 m//s^(2)`
B. `4 m//s^(2)`
C. `6 m//s^(2)`
D. None of these

Answer

A

Explanation

`(4T) a_(A)=(2T)(a_(B))`
`rArr a_(A)=a_(B)/2`
but `a_(B)=(dv_(B))/(dt)`
`=t+t^(2)/2 rArr a_(A)=t/2+t^(2)/4`
At `t=2s`,
`a_(A)=2/2+((2)^(2))/4 1+1=2 ms^(-2)`