A body of mass 1 kg begins to move under the action of a time dependent force $$\overrightarrow F = \left( {2t\widehat i + 3{t^2}\widehat J} \right)N,$$ where $${\widehat i}$$ and $${\widehat j}$$ are unit vectors along x and y axis. What power will be developed by the force at the time t ?

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic enegy of the particle becomes equal to 8 $$ \times $$ 10^$$-$$4 J by the end of the second revoluation after the beginning of the motion ?

Two particles A and B, move with constant velocities $$\overrightarrow {{v_1}} $$ and $$\overrightarrow {{v_2}} $$. At the initial moment their position vectors are $$\overrightarrow {{r_1}} $$ and $$\overrightarrow {{r_2}} $$ respectively. The condition for particles A and B for their collision is

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v₀. It collides with the ground, losses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v₀ is
(Take g = 10 m s^$$-$$2)