Two boys are standing at points A and B on ground where distance AB = a. The boy at point B starts running perpendicular to line AB with velocity '$V_1$'. The boy at point A starts running simultaneously with velocity 'V' and catches the other boy in time 't'. The value of 't' is

A particle is moving with constant angular acceleration $4\,\text{rad/s}^2$ in circular path. At what time the magnitudes of its tangential acceleration and centripetal acceleration will be equal ?

A particle describes a horizontal circle of radius 'r' in conical funnel with smooth inner surface with a speed of $0.5$ m/s. The height of the plane of the circle from the vertex of the funnel is (acceleration due to gravity, $g = 10\,\text{m/s}^2$)

A block of mass 'm' moving on a frictionless horizontal surface collides with a spring of spring constant 'K' and compresses it through a distance 'x'. The maximum momentum of the block after collision is