A particle is projected from a horizontal plane such that its velocity vector at time $t$ is given by $\vec v = a\hat i + (b - ct)\hat j$ . Its range on the horizontal plane is given by

A body slides down a frictionless track which ends in a circular loop of diameter $D$, then the minimum height $h$ of the body in term of $D$ so that it may just complete the loop, is

Average velocity of a particle is projectile motion between its starting point and the highest point of its trajectory is : (projection speed = $u$, angle of projection from horizontal= $\theta$)

The $x-t$ graph of a particle moving along a straight line is shown in figure The distance-time graph of the particle is correctly shown by

The $x-t$ graph of a particle moving along a straight line is shown in figure The $a-t$ graph of the particle is correctly shown by

A particle of mass $m$ is projected with a velocity $V$ making an angle of $45^o$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is