A $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N\, m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $\mathrm{m}/ \mathrm{s}$   $(g = 10\, m/s^2$)

Work equal to $25\,J$ is done on a mass of $2\,kg$ to set it in motion. If whole of it is used to increase the kinetic energy then velocity acquired by the mass is ............ $\mathrm{m}/ \mathrm{s}$

A particle of mass $m$ at rest is acted upon by a force $P$ for a time $t.$ Its kinetic energy after an interval $t$ is

A force $F$ acting on an object varies with distance $x$ as shown in the figure. The work done by the force in moving the object from $x = 0$ to $x = 8\,m$ is  ......... $J$

A boy holds a uniform chain of length $2\,m$ which is kept on a smooth table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table .............. $\mathrm{J}$

The potential energy of a body of mass $m$ is:
                      $U = ax + by$
Where $x$ and $y$ are position co-ordinates of the particle. The acceleration of the particle is