Given $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$. How much distance in $cm$ will $m_2$ cover in $0.4 \, s$?

$A$ car of mass $500\, kg$ is driven with acceleration $1\, m/s^2$ along a straight level road against a constant external resistance of $1000\, N$. When the velocity is $5\, m/s$,the rate at which the engine is working is .............. $kW$.

Two pulley arrangements shown in the figure are identical. The mass of the rope is negligible. In figure $(a)$,the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In figure $(b)$,$m$ is lifted up by pulling the other end of the rope with a constant downward force $F = 2mg$. The accelerations of $m$ in the two cases are respectively:

Two blocks of mass $2 \ kg$ and $1 \ kg$ are connected by an ideal spring on a rough surface. The spring is unstretched. The spring constant is $8 \ N/m$. The coefficient of friction is $\mu = 0.8$. Now,the $2 \ kg$ block is imparted a velocity $u$ towards the $1 \ kg$ block. Find the maximum value of velocity $u$ of the $2 \ kg$ block such that the $1 \ kg$ block never moves.

An ideal spring is connected between two blocks of masses $M$ and $m$. This system can move on a smooth horizontal table. The blocks are brought closer to compress the spring and then released. In the subsequent motion,select the true statement$(s)$:
$(a)$ They move in opposite directions with speeds inversely proportional to their masses.
$(b)$ The ratio of their speeds remains constant.
$(c)$ Linear momentum and energy of the system remain conserved.

If $M_2 = 2M_1$ and $\theta = 30^\circ$,the acceleration of $M_2$ is $a$. If the positions of the blocks are interchanged,what will be the acceleration of $M_2$?