$A$ particle of mass $m$ falls from rest through a resistive medium having a resistive force,$F = -kv$,where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity $(v)$ versus time $(t)$?

Two carts are pushed apart by the explosion of a charge placed between them. $A$ cart of mass $100 \ kg$ stops after traveling a distance of $18 \ m$. What distance will a cart of mass $300 \ kg$ travel before stopping? The coefficient of friction $\mu$ between the carts and the ground is the same for both.

$A$ uniform rod $AB$ of weight $100 \, N$ rests on a rough peg at $C$ and a force $F$ acts at $A$ as shown in the figure. If $BC = CM$ and $\tan \alpha = 4/3$,the minimum coefficient of friction at $C$ is:

$A$ truck starting from rest moves with an acceleration of $5 \ m/s^2$ for $1 \ s$ and then moves with constant velocity. The velocity $v/s$ time graph for the block on the truck with respect to the ground is: (Assume that the block does not fall off the truck and the coefficient of friction $\mu = 0.2$,$g = 10 \ m/s^2$)

$A$ bullet of mass $20 \, g$ travelling horizontally with a speed of $500 \, m/s$ passes through a wooden block of mass $10.0 \, kg$ initially at rest on a surface. The bullet emerges with a speed of $100 \, m/s$ and the block slides $20 \, cm$ on the surface before coming to rest. Find the coefficient of friction between the block and the surface. $(g = 10 \, m/s^2)$

Two fixed frictionless inclined planes making an angle $30^\circ$ and $60^\circ$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?