A particle of mass m_{1} and velocity v collides elastically (in one dimension) with a stationary particle of mass m_{2}. What are the velocities of m_{1} and m_{2} after the collision?


A particle of mass m_{1 }and velocity v collides elastically with a particle of mass m_{2}, initially at rest. 
After the collision, m_{1} has velocity v_{1}, and m_{2} has velocity v_{2}. What are v_{1} and v_{2}? 
Also, since the collision is elastic, the total kinetic energy of the system is conserved.
(Equation 2)
Equations 1 and 2 form a system of 2 equations with 2 unknowns (v_{1} and v_{2}). All you have to do is solve it. Alternatively, you can remember the solution for the general case.