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 $m/s$):

Shown in the diagram is a system of two bodies,a block of mass $m$ and a disc of mass $4m$,held in equilibrium. If the string $3$ is burnt,find the acceleration of the disc. Neglect the masses of the pulleys $P$ and $Q$. The coefficient of friction between the block and the horizontal surface is $0.5$ and the friction between the disc and the string is zero. (Take $g = 10 \ m/s^2$)

$A$ uniform cube of side $b$ and mass $M$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point at a height $3b/4$ above the base. What should be the coefficient of friction $\mu$ between the cube and the table so that it will tip about an edge before it starts slipping?

$A$ force of $(2.6 \hat{i} + 1.6 \hat{j}) \text{ N}$ acts on a body of mass $2 \text{ kg}$. If the velocity of the body at time $t = 0$ is $(3.6 \hat{i} - 4.8 \hat{j}) \text{ ms}^{-1}$, the time at which the body will just have a velocity along the $x$-axis only is: (in $\text{ s}$)

$A$ spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released,the spring exerts an equal and opposite force on each cart for the same time $t$. If the coefficient of friction $\mu$ between the ground and the carts is the same,find the ratio of the displacements of the two toy carts.

$A$ car accelerates on a horizontal road due to the forces exerted by