A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:

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

The work done by a force $\vec F = (-6x^3\hat i)\, N$, in displacing a particle from $x = 4\, m$ to $x = -2\, m$ is .............. $\mathrm{J}$

A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ..............  $\mathrm{m} / \mathrm{s}$

Two identical particles are moving with same velocity $v$ as shown in figure. If the  collision is completely inelastic then

A particle fall from height $h$ on $a$ static horizontal plane rebounds. If $e$ is coefficient of  restitution then before coming to rest the total distance travelled during rebounds will  be:-