A ball is projected from ground at an angle of $\theta $ from horizontal then graph of kinetic energy and time will be

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1\,m/s$ so as to have same K.E. as that of the boy. The original speed of the man will be

An object of mass ' $m$ ' initially at rest on a smooth horizontal plane starts moving under the action of force $F=2 N$. In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta= kx$, where $k$ is a constant and $x$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $E =\frac{ n }{ k } \sin \theta$. The value of $n$ is $.....$

A body of mass $2\, kg$ is thrown up vertically with K.E. of $490$  joules. If the acceleration due to gravity is $9.8$$m/{s^2}$, then the height at which the K.E. of the body becomes half its original value is given by ............ $\mathrm{m}$

If the kinetic energy of a body increases by $0.1\%$, the percent increase of its momentum will be .............. $\%$

A body moving with velocity $v$ has momentum and kinetic energy numerically equal. What is the value of $v$ ........$m/s$