Find the velocity of `c.m.`

Two blocks A and B of masses m and 2m are connected by a massless spring of natural length L and spring constant k . The blocks are intially resting on a smooth horizontal floor with the spring at its natural length , as shown . A third identical block C of mass m moves on the floor with a speed v_(0) along the line joining A and B and collides elastically with A . FInd (a) the velocity of c.m. of system (block A + B + spri ng) and (b) the minimum compression of spring.

The rain is falling vertically downward with velocity 6m//s and a man is moving horizontally with velocity 8m//s . Find the velocity of rain with respect to the man.

A particle executes S.H.M with amplitude of 10 cm and period of 10 s. Find the velocity of the particle at a distance 5 cm from the equilibrium position.

The r.m.s. velocity of oxygen molecules at 273K is 460 m//s . Find the r.m.s. velocity of argon at 40^(@)C .

If the refractive index of diamond is 2.4 find the velocity of light in diamond.(c= 3xx10^(8) m/s)

A particle starting with initial velocity of 30m/sec moves with a uniform acceleration of 9m/sec2. Find :(a) the velocity of the particle after 6 seconds.(b) how far it will go in 9 seconds.(c) its velocity when is has traversed 150m.