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 $\frac{dK}{dt}=\gamma t$, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

A ball of mass $0.2 \mathrm{kg}$ is thrown vertically upward by applying a force by hand. If the hand moves $0.2 \mathrm{m}$ while applying the force and the ball goes up to $2 \mathrm{m}$ height further, find the magnitude of the force. Consider $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

An athlete in the Olympic Games covers a distance of $100 \mathrm{m}$ in $10 \mathrm{s}$. His kinetic energy can be estimated to be in the range

When a rubber-band is stretched by a distance $x$, it exerts a restoring force of magnitude $F=ax+b{x}^2$ where a and b are constants. The work done in stretching the un stretched rubber-band by $L$ is

A point particle of mass $m$, moves along the uniformly rough track $PQR$ as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu$. The particle is released, from rest, from the point $P$ and it comes to rest at a point $R$. The energies, lost by the ball, over the parts, $PQ$ and $QR$, of the track, are equal to each other, and no energy is lost when particle changes direction from $PQ$ to $QR$. The values of the coefficient of friction $\mu$ and the distance $x\left(=QR\right)$ are, respectively, close to