$A$ body of mass $10 \,kg$ is kept on a rough horizontal surface with a coefficient of friction of $0.3$. If a horizontal force of $50 \,N$ is applied to the body, then the acceleration of the body is (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-2}$)

$A$ horizontal force of $129.4 \, N$ is applied on a $10 \, kg$ block which rests on a horizontal surface. If the coefficient of friction is $0.3$,the acceleration should be ....... $m/s^2$.

$A$ vehicle of mass $M$ is moving with momentum $P$ on a rough horizontal road. The coefficient of friction between the tyres and the horizontal road is $\mu$. The stopping distance is ($g$ $=$ acceleration due to gravity).

$A$ block of mass $5 \,kg$ is pulled by a force $F$ as shown in the figure. If the coefficient of friction is $0.1$, then the force needed to accelerate the block to $3 \,m/s^2$ to the right is close to (in $\,N$)

$A$ $300 \ kg$ crate is dropped vertically onto a conveyor belt that is moving at $1.20 \ m/s$. $A$ motor maintains the belt's constant speed. The belt initially slides under the crate,with a coefficient of friction of $0.400$. After a short time,the crate is moving at the speed of the belt. During the period in which the crate is being accelerated,find the work done by the motor which drives the belt.

What is the maximum value of the force $F$ such that the block shown in the arrangement does not move (in $N$)? (Given $m = \sqrt{3} \ kg$,$\mu = \frac{1}{2\sqrt{3}}$,$g = 10 \ m/s^2$)