Which of the following graphs is correct between kinetic energy $ (E), $ potential energy $(U)$  and height $(h)$ from the ground of the particle

Given that a force $\vec F$ acts on a body for time $t_1$ and displaces the body by $\vec d$ . In which of the following cases the velocity of the body must increase?

Power on $a$ mass is $P = (3t^2 -2t + 1)$ watt change in kinetic energy in $t = 2sec$ to $t = 4sec$ is :- .................... $\mathrm{J}$

An engine is attached to a wagon through a shock absorber of length $1.5\, {m}$. The system with a total mass of $40,000\, {kg}$ is moving with a speed of $72\, {kmh}^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0\, {m}$. If $90\, \%$ of energy of the wagon is lost due to friction, the spring constant is $....\, \times 10^{5}\, {N} / {m}$

A particle of mass $500 \,gm$ is moving in a straight line with velocity $v=b x^{5 / 2}$. The work done by the net force during its displacement from $x=0$ to $x =4 \,m$ is ...................$J$ (Take $b =0.25 \,m ^{-3 / 2} s ^{-1}$ )

A small bar starts sliding down on inclined plane forming an angle $\theta $ with the horizontal. The friction coefficient depends on the distance $x$ covered as $\mu  = kx$ , where $k$ is a constant. Find the distance covered by the bar till it stops