Consider the following statements $A$ and $B$ and identify the correct answer given below:
$(A)$ $A$ body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time.
$(B)$ When a body is at rest, it must be in equilibrium.

Which of the following statements is not true?

$A$ 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 $\text{ s}$)

$A$ parachutist of weight $w$ strikes the ground with his legs fixed and comes to rest with an upward acceleration of magnitude $3g$. The force exerted on him by the ground during landing is:

Two blocks $1$ and $2$ of equal mass $m$ are connected by an ideal string over a frictionless pulley. The blocks are attached to the ground by springs having spring constants $k_1$ and $k_2$ such that $k_1 > k_2$. Initially,both springs are unstretched. Block $1$ is slowly pulled down a distance $x$ and released. Just after the release,the possible values of the magnitudes of the accelerations of the blocks $a_1$ and $a_2$ can be

$A$ balloon of mass $M$ is descending at a constant acceleration $\alpha$. When a mass $m$ is released from the balloon,it starts rising with the same acceleration $\alpha$. Assuming that its volume does not change,what is the value of $m$?