A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK / dt =\gamma$ t, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

$(A)$ The force applied on the particle is constant

$(B)$ The speed of the particle is proportional to time

$(C)$ The distance of the particle from the origin increases linearly with time

$(D)$ The force is conservative

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 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 cricket ball is hit at ${30^o}$ with the horizontal with kinetic energy $K$. The kinetic energy at the highest point is

A stationary particle explodes into two particles of masses $x$ and $y$, which move in opposite directions with velocity $v_1$ and $v_2$. The ratio of their kinetic energies $\left(E_1: E_2\right)$ is

A light and a heavy body have equal kinetic energy. Which one has a greater momentum ?