$A$ car accelerates on a horizontal road due to the forces exerted by

$A$ force $F = Kt$ (where $t$ is the time in seconds and $K = 2 \, N/s$) is applied on a $2 \, kg$ block at $t = 0$ as shown in the figure. The displacement of the $8 \, kg$ block until the time when the $2 \, kg$ block starts slipping on the $8 \, kg$ block will be (coefficient of friction between the $2 \, kg$ block and the $8 \, kg$ block is $0.2$ and between the $8 \, kg$ block and the surface is zero,$g = 10 \, m/s^2$).

Two carts of masses $200 \, kg$ and $300 \, kg$ on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails is the same. If the $200 \, kg$ cart travels a distance of $36 \, m$ and stops,then the distance travelled by the cart weighing $300 \, kg$ is ........ $m$.

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 $B$?

Four blocks $A, B, C$ and $D$ of masses $6 \,kg, 3 \,kg, 6 \,kg$ and $1 \,kg$ respectively are connected by light strings passing over frictionless pulleys as shown in the figure. The strings $P$ and $Q$ are horizontal. The coefficient of friction between the horizontal surface and the block $B$ is $0.2$ and the blocks $A$ and $B$ move together. If the system is released from rest, then the tension in the string $Q$ is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,N$)

$A$ force acts for $20\,s$ on a body of mass $20\,kg$,starting from rest,after which the force ceases and the body travels $50\,m$ in the next $10\,s$. The value of the force is $..........\,N$.