Find the velocity of block $B$ at the instant shown in the figure (in $m/s$).

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

The machine as shown has $2$ rods of length $1\, m$ connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller moves back and forth,a $2\, kg$ weight moves up and down. If the roller is moving towards the right at a constant speed,the weight moves up with a:

In the pulley system shown in the figure,the mass of $A$ is half of that of $\text{rod } B$. The rod length is $500 \text{ cm}$. The mass of pulleys and the threads may be neglected. The mass $A$ is set at the same level as the lower end of the rod and then released. After releasing the mass $A$,it would reach the top end of the rod $B$ in time (Assume $g=10 \text{ m/s}^2$): (in $\text{ s}$)

$A$ block is dragged on a smooth plane with the help of a rope which moves with a velocity $v$ as shown in the figure. The horizontal velocity of the block is

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