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 ?

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 ?

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle $$\theta $$ to its initial direction and has a speed $${v \over 3}.$$ The second block's speed after the collision is