In the given figure the acceleration of $M$ is $(g = 10 \,ms^{-2})$

A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ -direction. Its speed $v(t)$ is depicted by which of  the  following curves ?

A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta>\mu$. The block is held stationary by applying a force $\mathrm{P}$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $\mathrm{P}$ is varied from $\mathrm{P}_1=$ $m g(\sin \theta-\mu \cos \theta)$ to $P_2=m g(\sin \theta+\mu \cos \theta)$, the frictional force $f$ versus $P$ graph will look like

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, the coefficient of friction between the block and the surface. $(g = 10\, m/s^2)$

A force $\vec{F}=\hat{i}+4 \hat{j}$ acts on the block shown. The force of friction acting on the block is

$A$ block $P$ of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on $P$ and connected to the wall with the help of a spring of spring constant k as shown in the figure. ${\mu _s}$ is the coefficient of friction between$  P$ and $ Q$. The blocks move together performing SHM of amplitude $A$. The maximum value of the friction force between $P$ and $Q$ is