This might be a very basic concept but I have never been able to understand it. 

Lets say a object with speed $v$ collides with another of same mass at rest in an perfectly inelastic collision in which the momentum. Why does then the both object join and move with speed $v/2$ ? If all the kinetic energy is lost then where does the energy to move the two blocks come from ? Also if I throw wet clay at my bedroom wall it does not move with the clay ?

I understand, plugging values in conservation of momentum equation gives this result.