Graph shows the acceleration of a $3 \mathrm{kg}$ particle as an applied force moves it from rest along $x-$axis. The total work done by the force on the particle by the time the particle reaches $x=6 \mathrm{m}$, is equal to

A particle is displaced from $x=+3 \mathrm{m}$ to $x=-3 \mathrm{m}$. The variation of force with position is given in the graph. Work done by this force during the displacement is,

Two identical blocks $A$ and $B$ are placed on two inclined planes as shown in the diagram. Neglect air resistance and friction.

Read the following statements and choose the correct options.

Statements $\mathrm{I}:$ Kinetic energy of $A$ on sliding to $J$ will be greater than the kinetic energy of $B$ on falling to $M$.

Statements $\mathrm{II}:$ Acceleration of $A$ will be greater than acceleration of $B$ when both are released to slide on inclined plane.

Statements $\mathrm{III}:$ Work done by external agent to move the block slowly from position $B$ to $O$ is negative.

Two blocks, $m_1=5 \mathrm{kg}$ and ${\mathrm{m}}_2=2 \mathrm{kg}$ are connected at the two ends of a spring of force constant, $k=100 \mathrm{N} {\mathrm{m}}^{-1}$. Friction coefficient between $m_1$ and ground is $0.4$ and between $m_2$ and ground is $0.2$. The minimum horizontal velocity $v$ that must be imparted to the $m_2$ towards right in order to just move $m_1$ over surface is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$,