In the given figure, the blocks $A$, $B$, and $C$ weigh $4 \ kg$, $6 \ kg$, and $8 \ kg$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is . . . . . . $N$. (Use $g = 10 \ m/s^2$)

$A$ 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 $..........\,N$.

$A$ $500 \, kg$ horse pulls a cart of mass $1500 \, kg$ along a level road with an acceleration of $1 \, m/s^2$. If the coefficient of sliding friction is $0.2$,then the force exerted by the horse in the forward direction is ......... $N$.

Explain why
$(a)$ a horse cannot pull a cart and run in empty space,
$(b)$ passengers are thrown forward from their seats when a speeding bus stops suddenly,
$(c)$ it is easier to pull a lawn mower than to push it,
$(d)$ a cricketer moves his hands backwards while holding a catch.

$A$ block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$,by a force $F = 20\, N$,making an angle of $30^o$ with the horizontal,as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block,in case $(B)$ and case $(A)$ will be ........ $ms^{-2}$ .$(g = 10\, ms^{-2})$

What is the acceleration of the block and trolley system shown in the figure,if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.