The masses of the blocks A and B are m and M, respectively. Between A and B there is a constant frictional force F, and B can slide frictionlessly on horizontal surface. A is set in motion with velocity v0 while B is at rest. What is the distance moved by A relative to B before they move with the same velocity?

Free-body diagrams (figure)Equations of motion:         aB=FM( in +x direction )aA=Fm( in −x direction )Relative acceleration of A w.r.t. B :         a→A,B=a→A−a→B=−Fm−FM=−Fm+MmM (along −x direction) Initial relative velocity of A w.r.t. B        uA,B=v0Final relative velocity of A w.r.t. B = 0Using v2=u2+2as          0=v02−2F(m+M)mMS ⇒ S=Mmv022F(m+M)