The velocity of end ' $A$ ' of rigid rod placed between two smooth vertical walls moves with velocity ' $u$ ' along vertical direction. Find out the velocity of end ' $B$ ' of that rod, rod always remains in constant with the vertical walls.

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

The velocities of $A$ and $B$ are marked in the figure. The velocity of block $C$ is  ......... $m/s$ (assume that the pulleys are ideal and string inextensible)

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction, as shown in figure. If the trolley is accelerated horizontally along the positive $x$ -axis with $a_0$, then If $a_{min}$ and $a_{max}$ are the minimum and maximum values of $a_0$ for which the blocks remain stationary with respect to the surface, then identify the correct statements

Two particles $A$ and $B$ are connected by rigid rod $A B$. The rod slides along perpendicular rails as shown here. The velocity of $A$ to the left is $10\; m / s$. What is the velocity of $B$(in $m/s$) when angle $\alpha=60^{\circ}$?

In the figure shown the velocity of different blocks is shown. The velocity of $C$ is $.........\,m/s$