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.

Five persons $A, B, C, D$ and $E$ are pulling a cart of mass $100 \, kg$ on a smooth surface and the cart is moving with an acceleration of $3 \, m/s^2$ in the east direction. When person $A$ stops pulling,it moves with an acceleration of $1 \, m/s^2$ in the west direction. When person $B$ stops pulling,it moves with an acceleration of $24 \, m/s^2$ in the north direction. The magnitude of the acceleration of the cart when only $A$ and $B$ pull the cart,keeping their directions the same as the original directions,is ............ $m/s^2$.

$A$ block $A$ of mass $m_1$ rests on a horizontal table. $A$ light string connected to it passes over a frictionless pulley at the edge of the table,and from its other end,another block $B$ of mass $m_2$ is suspended. The coefficient of kinetic friction between the block $A$ and the table is $\mu_k$. When the block $A$ is sliding on the table,the tension in the string is:

In the figure,a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_1$ and that between the floor and the ladder is $\mu_2$. The normal reaction of the wall on the ladder is $N_1$ and that of the floor is $N_2$. If the ladder is about to slip,then

$A$ packet of weight $W$ dropped from a parachute strikes the ground and comes to rest with retardation equal to twice the acceleration due to gravity. The force exerted on the ground is

$A$ $2 \, kg$ mass starts from rest on a smooth inclined surface with an inclination of $30^\circ$ and a length of $2 \, m$. What distance $S$ (in meters) will it travel before coming to rest on a rough horizontal surface with a coefficient of friction of $0.25$?