Find the velocity of the centre of mass of two identical particles moving with velocities `v_(1) and v_(2) `

Show that in absence of any external force the centre of mass of two moving particles moves with uniform velocity.

A particle travels half of the distance between A and B with a velocity v_(0) . During half of the time required to travel the remaining distance the particle moves with a velocity v_(1) and the rest with a velocity v_(2) . Find the average velocity of the particle.

Find the expression for the kinetic energy of an object of mass m, moving with velocity v.

A particle starting from a point A and moving with a positive constant acceleration along a straight line reaches another point B is time T. Suppose that the initial velocity of the particle is u gt0 and P is the midpoint of the line AB. If the velocity of the particle at point P is v_(1) and if the velocity at time (T)/(2) is v_(2) , then -

Dimensionally prove the expression (mv^(2))/( r) for the centripetal force F acting on a particle of mass m moving with velocity v in a circle of radius r.

A body of mass m moving with a velocity u strikes elastically a stationary body of mass 2m . After the elastic collision the bodies move with velocities v and V respectively . Show that the body of mass m loses 8/9 part of its initial kinetic energy.