On the horizontal surface of a truck,a block of mass $1 \; kg$ is placed $(\mu = 0.6)$. If the truck is moving with an acceleration of $5 \; m/s^2$,then the frictional force on the block will be: (in $; N$)

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 of mass $M = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $\mu = 0.05.$ When hit by a bullet of mass $m = 50\,g$ moving with speed $v,$ which gets embedded in it,the block moves and comes to a stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,m/s^2,$ the value of $H$ is close to ................. $km$.

An ideal spring is connected between two blocks of masses $M$ and $m$. This system can move on a smooth horizontal table. The blocks are brought closer to compress the spring and then released. In the subsequent motion,select the true statement$(s)$:
$(a)$ They move in opposite directions with speeds inversely proportional to their masses.
$(b)$ The ratio of their speeds remains constant.
$(c)$ Linear momentum and energy of the system remain conserved.

$A$ body of mass $2 \ kg$ is initially at rest. It moves on a table under the influence of a horizontal force of $7 \ N$. If the coefficient of kinetic friction is $0.1$,then the work done by the applied force and the work done by the frictional force in $10 \ s$ are respectively:

The graph below shows the variation of a force $F$ with time $t$ on a body which is moving in a straight line. The dependence of force on time is $F \propto t^{n}$. Initially,the body is at rest. If the speed of the object is $2 \, m/s$ at $3 \, s$,then the speed at $4 \, s$ will be approximately (in $m/s$):