A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when

A uniform force of $$\left( {3\widehat i + \widehat j} \right)$$ newton acts on a particle of mass 2 kg. Hence the particle is displaced from position $$\left( {2\widehat i + \widehat k} \right)$$ metre to position $$\left( {4\widehat i + 3\widehat j - \widehat k} \right)$$ metre. The work done by the force on the particle is

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P₀. The instantaneous velocity of this car is proportional to

The potential energy of a particle in a force field is $$U = {A \over {{r^2}}} - {B \over r}$$ where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is