$A$ 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:

$A$ particle of mass $m$ falls from rest through a resistive medium having a resistive force,$F = -kv$,where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity $(v)$ versus time $(t)$?

For the given system,find the tension $T_2$ in the upper string.

$A$ block of mass $m$ is moving with a constant acceleration $a$ on a rough plane. If the coefficient of friction between the block and the ground is $\mu$,the power delivered by the external agent after a time $t$ from the beginning is equal to:

$A$ block of mass $15 \;kg$ is placed on a long trolley. The coefficient of static friction between the block and the trolley is $0.18$. The trolley accelerates from rest with $0.5 \;m s^{-2}$ for $20 \;s$ and then moves with uniform velocity. Discuss the motion of the block as viewed by
$(a)$ a stationary observer on the ground,
$(b)$ an observer moving with the trolley.

Two pulley arrangements shown in the figure are identical. The mass of the rope is negligible. In figure $(a)$,the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In figure $(b)$,$m$ is lifted up by pulling the other end of the rope with a constant downward force $F = 2mg$. The accelerations of $m$ in the two cases are respectively: