Statement I An object subjected to velocities $\mathbf{v}_1$ and $\mathbf{v}_2$ has a resultant velocity with magnitude $|\mathbf{v}|=\left|\mathbf{v}_1\right|+\left|\mathbf{v}_2\right|$.

Statement II The magnitude of displacement is either less or equal to the path length of an object between two points.

Statement III The instantaeous acceleration is the limiting value of the average acceleration as the time interval approaches zero.

Which of the following is correct?

For a projectile, if $\alpha$ is the angle of projection, $R$ is the range, $h$ is the maximum height, $t$ is the time of flight then

At time $t=0$, a force $F=\alpha t$, where $t$ is time in seconds, is applied to a body of mass 1 kg , resting on a smooth horizontal plane. If the direction of the force makes an angle of $45^{\circ}$ with the horizontal, then the velocity of the body at the moment of its breaking off the plane is

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?