An object of mass ' $m$ ' initially at rest on a smooth horizontal plane starts moving under the action of force $F=2 N$. In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta= kx$, where $k$ is a constant and $x$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $E =\frac{ n }{ k } \sin \theta$. The value of $n$ is $.....$

A shell of mass $200\, gm$ is ejected from a gun of  mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $\mathrm{ms}^{-1}$

Which of the following statements is correct ?

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1\,m/s$ so as to have same K.E. as that of the boy. The original speed of the man will be

A spherical body of mass $2\,kg$ starting from rest acquires a kinetic energy of $10000\,J$ at the end of $5^{\text {th }}$ second. The force acted on the body is $.....N$

Tripling the speed of the motor car multiplies the distance needed for stopping it by