Momentum:difference in final velocities

[Sprinkle159]

If the initial velocities of 2 particles are given, and the masses are equal, then is there some limit on what the final velocities can be?

m₁v_1i+m₂v_2i=m₁v_1F+m₂v_2F

(initial velocity of particle 2 is zero; v_2i=0)

v_1i=v_1F+v_2F

To clarify my question if particle 1 has an initial velocity of 50 m/s, then this equation says the final velocity of particle 1 could be -550 m/s, and then the final velocity of particle 2 would be 600 m/s, which are much larger then the initial velocity of particle 1. So is there some limit on what values the final velocities can have?

 

[Stonebridge]

Yes. The collision would also need to satisfy conservation of energy.

 

[Saw]

... and that means that (in your example, where the masses are equal and particle 2 is initially at rest with the reference frame), there are two extreme possibilities [particle 1 stops and particle 2 takes particle's 1 initial velocity (perfectly elastic collision) and both particles stick to each other and move with velocity = 0.25 m/s (perfectly inelastic collision)] and a range between them but not beyond.