In what distance will body $A$ of figure attain a velocity of $3 m/s$ starting from rest ? Take $\mu =0.2.$ Pulleys are fric-tionless and massless.

If $a$ is the acceleration of the block $A$ then acceleration of block $B$ will be $\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$. Thus

$150 g\sin \left({\theta }_1\right)-\left(T+\mu \times 150\cos \left({\theta }_1\right)\right)=150a$      …. (1)

and

$T\text{'}-(200 g\sin \left({\theta }_2\right)+\mu \times 200\cos \left({\theta }_2\right)=200a$      …. (2)

Also T' = 2T  ………………………………………………(3)

The velocity of the block $A,$

$v^2=2as$  

$\therefore s=\frac{v^2}{2a}$                                                             …. (4)

After substituting the known values and simplifying, we get

$s=3.529 m$