$A$ block of mass $5\, kg$ is on a rough horizontal surface and is at rest. Now a force of $24\, N$ is imparted to it with negligible impulse. If the coefficient of kinetic friction is $0.4$ and $g = 9.8\, m/s^2$,then the acceleration of the block is ........ $m/s^2$.

$A$ car having a mass of $1000\, kg$ is moving at a speed of $30\, m/s$. Brakes are applied to bring the car to rest. If the frictional force between the tyres and the road surface is $5000\, N$,the car will come to rest in ........ $s$.

The power required for an engine to maintain a constant speed of $50 \,m \,s^{-1}$ for a train of mass $3 \times 10^6 \,kg$ on rough rails is (The coefficient of kinetic friction between the rails and wheels of the train is $0.05$ and acceleration due to gravity $= 10 \,m \,s^{-2}$).

$A$ conveyor belt is moving horizontally with a velocity of $2 \,m \,s^{-1}$. If a body of mass $10 \,kg$ is kept on it, then the distance travelled by the body before coming to rest relative to the belt is (The coefficient of kinetic friction between the belt and the body is $0.2$ and acceleration due to gravity is $10 \,m \,s^{-2}$) (in $\,m$)

$A$ block of mass $M = 5\,kg$ is resting on a rough horizontal surface for which the coefficient of friction is $0.2$. When a force $F = 40\,N$ is applied at an angle of $30^\circ$ with the horizontal,the acceleration of the block will be ........ $m/s^2$ $(g = 10\,m/s^2)$.

$A$ block of a certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are $0.4$ and $0.25$ respectively. $A$ constant horizontal force $F = 20 \text{ N}$ acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take $g = 10 \text{ m/s}^2$): (in $\text{ kg}$)