Statement I The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration.

Statement II From a height of 15 m , a ball is projected vertically upwards with a velocity of $30 \mathrm{~m} / \mathrm{s}$. If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is $30 \%$.

Statement III The velocity acquired by a body of mass $m$ after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass $m$.

Which of the following is correct?

An object is moving in a straight line under the influence of a source of constant power. If $v$ and $t$ are velocity and time respectively, then

A ball of mass 1 kg moves in a straight line with velocity $v=c x^\alpha$, where $c=1$ (SI unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x=0$ to $x=4 \mathrm{~m}$ is 128 J , then the $\alpha$ is

The potential energy of an object is $U(x)=\left(5 x^2-4 x^3\right) \mathrm{J}$, where $x$ is the position in metre. The position at which the force becomes zero is