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

Two spheres A and B of masses m₁ and m₂ respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity in a direction perpendicular to the original direction. The mass A moves after collision in the direction

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s^$$-$$1. It collides with a horizontal spring of force constant 200 N m^$$-$$1. The maximum compression produced in the spring will be

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