If the acceleration of block $A$ is $2\,m/s^2$ to the left and the acceleration of block $B$ is $1\,m/s^2$ to the left,then find the acceleration of block $C$.

If the blocks $A$ and $B$ are moving towards each other with accelerations $a$ and $b$ respectively,find the net acceleration of block $C$.

What is the acceleration of block $B$ for the given system?

$A$ basket and its contents have mass $M$. $A$ monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2 \, ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3 \, s$. How fast is the basket rising at the end of the $3 \, s$? Neglect the mass of the pulley and the rope. (given : $g = 32 \, ft/s^2$)

Two equal masses $A$ and $B$ are arranged as shown in the figure. The pulley and string are ideal and there is no friction. Block $A$ has a speed $u$ in the downward direction. The speed of the block $B$ is:

In the arrangement shown in the figure,the block of mass $m=2\,kg$ lies on the wedge of mass $M=8\,kg$. Find the initial acceleration of the wedge if the surfaces are smooth and the pulley and strings are massless.