An object of mass $1 \,kg$ moving on a horizontal surface with initial velocity $8 \,m/s$ comes to rest after $10 \,s$. If one wants to keep the object moving on the same surface with velocity $8 \,m/s$,the force required is ...... $N$.

$A$ block is projected with speed $20 \,m/s$ on a rough horizontal surface. The coefficient of friction $(\mu)$ between the surfaces varies with time $(t)$ as shown in the figure. The speed of the body at the end of $4 \,s$ will be ............ $m/s$ $(g = 10 \,m/s^2)$.

$A$ force $\vec{F}=\hat{i}+4 \hat{j}$ acts on the block shown in the figure. The force of friction acting on the block is (take $g=10 \, m/s^2$)

Consider a car moving on a straight road with a speed of $100\, m/s$. The distance at which the car can be stopped is ........ $m$. $[\mu_k = 0.5, g = 10\, m/s^2]$

$A$ body is moving along a horizontal surface with a velocity of $4 \,m/s$. If the coefficient of kinetic friction is $0.2$, the distance travelled by the body before coming to rest is $(g = 10 \,m/s^2)$. (in $\,m$)

$A$ man slides down a telegraphic pole with an acceleration equal to one-fourth of the acceleration due to gravity. The frictional force between the man and the pole is equal to which of the following in terms of the man's weight $w$?