# Momentum:difference in final velocities

• Sprinkle159

#### 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?

m1v1i+m2v2i=m1v1F+m2v2F

(initial velocity of particle 2 is zero; v2i=0)

v1i=v1F+v2F

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?

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

... 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.