An object is projected with kinetic energy $K$ from a point $A$ at an angle $60^{\circ}$ with the horizontal. In the absence of air friction, what is the ratio of the difference in kinetic energies at points $B$ and $C$ to the kinetic energy at point $A$ (see figure)?

$A$ body of mass '$m$' is projected with a speed '$u$' making an angle of $45^{\circ}$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{\sqrt{2} mu^3}{Xg}$. The value of '$X$' is

$A$ block of mass $5\,kg$ is moving horizontally at a speed of $1.5\,m/s$. $A$ perpendicular force of $5\,N$ acts on it for $4\,s$. What will be the distance of the block from the point where the force started acting?

An athlete completes one round of a circular track of radius $10 \, m$ in $40 \, sec$. The distance covered by him in $2 \, min \ 20 \, sec$ is ........ $m$.

$A$ frictionless circular wire of unit radius is fixed on the horizontal plane. Two point particles of unit mass start moving simultaneously from point $A(\theta = \pi/2)$ with identical uniform angular speeds in opposite directions, and meet again at point $B(\theta = -\pi/2)$. During this time, which of the following figures schematically represent the magnitude of the total linear momentum $P$ of the system, as a function of $\theta$?

At any time $t$,the coordinates of a moving particle are $x = at^2$ and $y = bt^2$. The speed of the particle is